The first method is to enrich natural uranium by separating U-235 from U-238. The U-235 isotope is fissile, but makes up only 0.72% of natural uranium by mass. If uranium is to be used in a bomb, its U-235 concentration must be raised to 90%. The second method is to bombard natural uranium with neutrons and transmute it into plutonium. The U-238 isotope is fertile, and if it captures a neutron, it will turn into U-239, which then decays into Pu-239. If plutonium is to be used in a bomb, its Pu-239 concentration must be raised to 93%. Uranium can be enriched to weapons grade by a variety of techniques, but uranium can only be transmuted into plutonium by a reactor. In hindsight, the German nuclear program made significant steps towards uranium enrichment, but were lagging in their efforts to make a reactor. The details of this subject are complicated and sometimes convoluted, since many historians have offered many appraisals that are mutually exclusive. Authors like Samuel Goudsmit (of ALSOS fame) have such a prejudice against the nazis that it interferes with their ability to even tell a coherent narrative. Other writers go in completely the opposite direction, and try to credit the Germans with all kinds of specious achievements. As always, though, only some of these appraisals can be corroborated. This article will focus on a number of myths about the German nuclear program and how it measured up to the Manhattan project.
The B-VIII pile uranium pile in Haigerloch
The Uranverein was never able to develop an effective means of enriching uranium to weapons grade.
This is simply not true. Early in 1943, the research team under Paul Harteck had created a centrifuge of novel design, subdivided into multiple rotors and multiple chambers. This 'ultracentrifuge' was tested by separating isotopes of xenon gas, and then by separating uranium hexafluoride. This machine was able to enrich several grams of uranium to 7%, good enough to warrant funding from the Reich research council (RFR). More centrifuges were made, and the design was constantly tinkered with. By May of 1944, a company in Freiburg had built and successfully tested the MK III ultracentrifuge, which persuaded Harteck to move his laboratory there. The team set up a facility in the nearby town of Kandern, where a few centrifuges were assembled into a cascade. After a few months, however, allied bombings forced them to stop work and relocate to a town called Celle. Early in 1945, the facility only had 20 or so of these machines, but was still enriching 50 grams of uranium to 15% each day! The MK III ultracentrifuge was a technological marvel with a performance far exceeding the american centrifuges.  There were actually plans to put it into mass production, but the war ended before this could take place. Other research teams in germany had experienced similar ups and downs. By June of 1943, Erich Bagge had created an 'isotope-sluice' machine that ran uranium hexafluoride through two shutters revolving at high speed, allowing the lighter U-235 to be separated. This was a totally novel approach which never occurred to the Americans, using a combination of electromagnetism, centrifugal force, and thermal diffusion.
While his first two prototypes were destroyed by air raids, Bagge was able to relocate to Butzbach and set up another machine. By July of 1944, the 'isotope-sluice' had undergone an endurance test lasting 120 hours, yielding several grams of much enriched uranium. The models indicated its efficiency could be greatly increased. At around this same time, Manfred von Ardenne was testing a magnetic isotope separator, not unlike the calutrons used at the Y-12 plant at oak ridge. Both machines used magnetic fields to deflect charged particles and separate them based on differences in mass, but the German design used an ion source to sublimate the uranium. This greatly increased its enrichment capacity. Ardennes laboratory was located underground in his manor, which protected it from air raids. And since he was financially supported by the post office, work on it was able to continue unimpeded. Fortunately for the allies, however, only one of these machines were made during the war. Putting the technical details aside for now, it should be clear that the Uranverein had made major strides in their knowledge and ability to separate U-235 from U-238. The problem was that these efforts were all confined to laboratorys, and were never expanded to the industrial scale that was needed for an atom bomb. There were not enough scientists and engineers working on uranium enrichment, and there was not enough funding from the RRC to produce these machines in anywhere near the numbers required. The only team that came close was the one run by Harteck.
The german ultracentrifuge, which was
superior to the american design
German scientists were never able to achieve a self-sustaining nuclear reaction, much less a working reactor.
This point requires some background. One of the things needed for a nuclear reactor is a substance which can act as a neutron moderator, and allow a chain reaction to continue unabated. During WW2 there were only two known substances that could fulfill this role: Graphite and heavy water. Allied and axis scientists investigated each of them. In January 1941, Walther Bothe had performed experiments on the purest graphite available, to see whether it could slow down the neutrons without absorbing them. Eventually, he determined that the capture cross-section of graphite was too large to make it an effective moderator. The Americans actually came to the same conclusion as him, but would quickly learn that this was due to trace amounts of boron, which could be removed by making the graphite out of petroleum instead of coke. The Germans never did this extra step, and were now totally dependent on a supply of heavy water, which was synthesized at only one location in all of Europe: The Norsk hydro plant. By May of 1942, enough heavy water had been assembled to make a uranium pile at Leipzig. The L-IV experiment by Werner Heisenberg yielded a neutron increase of 13 percent, meaning that the pile emitted more neutrons than what had been injected into it. This was a step in the right direction.  Unfortunately, the containment vessel exploded soon after the experiment, leaving them with a shortage of heavy water. In April of 1943, Kurt Diebner performed an experiment of his own at a laboratory in Gottow. Rather than mix the uranium and heavy water together into an aluminum sphere, he had the uranium cast into cubes, and the heavy water frozen into ice. The G-II test ended with a neutron increase of 36 percent, 'an extremely favorable and unexpected result.'
Diebner had proven that uranium cubes were superior to the plates that Heisenberg used, and that the aluminum containment vessels were completely unsuitable. While the basic research problems had been overcome, no new reactors could be built without an adequate supply of heavy water. Progress on this area stalled as a consequence, and results came at an agonisingly slow pace. Conditions were only worsened when the allys conducted raids against the Norsk hydro plant, interrupting the supply of heavy water. The months and years dragged on, and optimism soon gave way to pessimism. By the spring of 1944, Heisenbergs team in Berlin finally went forward with the B-VI experiment, which had been delayed for roughly a year due to the bombings. After many months of testing and altering the layout of their uranium pile, they were unable to yield significantly higher results than Diebner. Thus, Heisenberg was forced to admit the inferiority of the plates, and to use a carbon reflector instead of light water. By the winter of 1944, they had no choice but to move their equipment to Haigerloch to avoid the relentless air raids. Diebners team had already evacuated from Gottow to Stadtilm for the same reason. By this time, they were carrying out the G-IV test which yielded the highest neutron increase of any German reactor. Diebner was elated with the results, later claiming that his pile had briefly went critical. In the spring of 1945, Heisenbergs team began their final experiment of the war. The B-VIII pile also obtained a high result: For every 100 neutrons injected into the pile, 670 neutrons were emitted at the surface. This was a very significant achievement, but it wasn't quite enough for a self sustaining reaction.
The German reactors were very unsafe, basically an accident waiting to happen: They had no control rods, and no way to stop a meltdown from taking place.
This criticism focuses on the final two 'reactors' created near the end of the war, which used uranium cubes and heavy water. The first was run by Kurt Diebners team at Stadtilm, while the second was run by Werner Heisenbergs team at Haigerloch. Both of these uranium piles were assembled under very difficult circumstances. The scientists were on the run from allied armys, and had to carry all the necessary supplys by truck. A containment vessel had been built prior to their arrival: This was a simple cavity excavated into the ground, and lined with carbon to act as a neutron reflector. When the experiments were actually ran, the Germans didn't use control rods: Their preparations were more haphazard. In the event of a dangerous thermal runaway, the scientists plan was to drop a lump of cadmium down the reactor chimney, which would smother the radium initiator. If this didn't shut the reaction down, their only option would be to open the cavity lid and remove the uranium cubes. This procedure could take up to 10 minutes. Most people therefore get the impression that the G-IV and B-VIII reactors were very dangerous, and could have undergone an explosive meltdown that would irradiate the entire area for centurys. This is completely false, however, because they are comparing a uranium pile to a full scale reactor. The one is related to the other by about the same amount that a toy truck is related to a caterpillar truck! A uranium pile operates at much lower power levels than a true reactor, and is physically incapable of 'melting down.' 
The B-VIII uranium pile, in all its glory
The Uranverein never measured the fission cross section of uranium-235: Hence, they were never able to properly estimate the critical mass for an atomic bomb.
That isn't supported by the facts. After the conquest of Denmark and France in mid 1940 (among other unfortunate victims of the blitzkrieg), Germany had access to cyclotrons at Vienna, Copenhagen, and Paris. These are a type of particle accelerator that can generate 'fast neutrons', and thus allow scientists to measure the fission cross section of an element. Each of the laboratorys in Vienna, Copenhagen, and Paris were visited by German teams during the war. This is unsurprising, because determining the critical mass of U-235 was a key parameter for which much of their work would hinge on. The scientists made fission cross section estimates at three points in the war, each more accurate than the last.  In August of 1941, an individual named Fritz Houtermanns (who was employed in the laboratory of Manfred von Ardenne) wrote a paper which discussed runaway chain reactions and the possibility of transmuting uranium into plutonium. This paper was circulated among members of the uranverein, eliciting a flurry of discussion. By February 1942, the HWA team had published a document outlining the critical mass for a U-235 bomb: The estimate was 10 to 100 kilograms. This was comparable to the estimate made by the NAS team in america, back in November of 1941. The baseless claims about the German scientists being unable to do these basic experiments were promulgated by authors like Samuel Goudsmit after the war, who despised the men for their deeds during the war.
After the destruction of the Norsk hydro plant in 1943, the germans were unable to produce heavy water, and were forced to rely on their existing stocks.
First off, the Norsk hydro plant was never fully destroyed. After the bomb raid of 1943, it was actually disassembled and shipped to Germany. Second, the scientists involved were always aware of the dangers of relying exclusively on one source of supply. That is why they set up four different plants over the course of the war. They even invented new hydrolytic techniques to produce more deuterium oxide at a lower price, which were eventually used in these facilitys. The first was the Leuna plant, south of Merseberg, which used the Harteck/Suess process (and was codenamed Stalins organ). The second was the Kiel plant using Dr Geibs hydrogen sulphide exchange process. Then the Hamburg plant, which used the Harteck low pressure distilation process. And finally, there was the Munich plant using the Clusius-Linde process. The west didn't learn about the existence of these facilitys until long after the wars end. The ALSOS mission by Samuel Goudsmit only ever knew about one of them: The Leuna plant run by IG farben, which was destroyed in a bomb raid on July 28, 1944. This was one of the reasons they underestimated the progress made by the uranverein.
 Although to be fair, funding for the centrifuge research was cancelled in 1943. Its possible that the Americans could have come up with a design that was as good as that of the Germans, but they never got the opportunity to do so.
 There were quite a few more tests after the L-IV experiment: There was the G-II to G-IV tests in Gottow, along with the B-VI to B-VIII in Berlin. Other teams may have carried out their own uranium pile experiments, as well.
 In fact, the German reactors were more safe than the Chicago pile tested by Enrico Fermi in 1942. The reason for this is that heavy water is a more effective moderator than graphite, which means their design used much less uranium to generate a chain reaction.
 Fritz Houtermans used radium to make the 'slow neutron' measurements in 1941. Walther Bothe used the Paris cyclotron to do the fast neutron measurements in 1942. Jentschke and Lintner used the Vienna cyclotron to do more fast neutron measurements in 1943.
The Virus House: Nazi Germany's Atomic Research and the Allied Countermeasures, by David Irving.
German National Socialism and the Quest for Nuclear Power: 1939-49, by Mark Walker.
Heavy Water and the Wartime Race for Nuclear Energy, by Per F. Dahl.
Hitler's Nuclear Weapons, by Geoffrey Brooks.