I thought the question had been answered definitively by the release of the Farm Hall transcripts (Operation Epsilon). In the spring and summer of 1945 ten of the leading German nuclear physicists, including Heisenberg, were sequestered at a house near Cambridge, England. The house was bugged, and there is no reason to doubt that the conversations recorded were genuine:
Diebner: "I wonder whether there are microphones installed here?"
Heisenberg: "Microphones installed? (laughing) Oh no, they're not as cute as all that. I don't think they know the real Gestapo methods; they're a bit old fashioned in that respect."
I read the transcripts a few years ago, and my impression was that Heisenberg had grossly overestimated the amount of U235 necessary for a bomb. Here is what appears in the Wikipedia entry on Farm Hall:
Most historians have no reason to believe that he was not being genuine, and the attitude of Heisenberg and the other scientists over all the months and especially their reaction to the shattering news of the bomb explosion was so genuine that it is almost inconceivable it was staged.
All of the scientists expressed shock when informed of the atomic bombing of Hiroshima on August 6, 1945. The transcripts seem to indicate that the physicists, in particular Heisenberg, had either overestimated the amount of enriched uranium that an atomic bomb would require or consciously overstated it, and that the German project was at best in a very early, theoretical stage of thinking about how atomic bombs would work.
Recently I came across an exchange in the NY Review of Books, between physicist Jeremey Bernstein, who wrote Hitler's Uranium Club: The Secret Recordings at Farm Hall, and Thomas Powers, author of Heisenberg's War. Powers believes that Heisenberg had a much better understanding of the requirements for a bomb than are suggested by his Farm Hall comments immediately after learning of Hiroshima.
[Bernstein:] ... In June of 1942 Heisenberg was asked how much uranium a nuclear bomb would use that could destroy London. If one kilogram of uranium could be completely fissioned it would produce an explosion equal to about twenty thousand tons of TNT; about the size of the Hiroshima bomb. This would correspond to a sphere of uranium with a radius of a little over two centimeters—a ping- pong ball. But in a real bomb only about 2 percent of the uranium is fissioned so that about a hundred kilograms of uranium are needed, which corresponds to a radius of about eight and a half centimeters. At Farm Hall Heisenberg did not seem to have a clear idea of the efficiency question, so it is totally unclear to me what he had in mind when, in 1942, he apparently indicated that it was the shape of a pineapple. ...
[Letter from Charles Frank, British physicist and intelligence advisor to Operation Epsilon]: As I remember it, Heisenberg gave just the calculation you quote, except that my memory says he reached the answer 5 tons.... He gave this calculation at the beginning of an elegant colloquium, delivered the day after they heard about Hiroshima, in which he used a rather polished version of diffusion-and-multiplication theory (which he was no doubt familiar with from their pile work) to arrive at an answer for critical mass of the order of 1 or a few kilograms. He gave the crude and faulty calculation at the beginning, as the way they had worked it out before, and I think he said it was the way he had worked it out, and I think he said it was the estimate he gave at the 1940 conference about what was to be done with nuclear fission in relation to the war. I think he said he had done the revised calculation overnight, and I think that the whole style of the lecture implied that he was presenting a result and argument new to him and to his audience.
[Powers:] Bernstein interprets Heisenberg's remarks, available to us since the 1992 release of the Farm Hall tapes recorded by British intelligence during the war, to mean that Heisenberg failed to calculate the critical mass of an atomic bomb earlier in the war. Because fissionable material is extremely difficult and expensive to manufacture, the amount of it necessary for a bomb—the "critical mass"—is by far the most important technical question to be asked before embarking on a bomb program. A figure on the order of tons would have made building a bomb impossible for any nation at the time, the United States included. From his interpretation of Heisenberg's remarks on this point Bernstein concludes there was no German bomb, and no German bomb program, as the result of "simple incompetence"—the phrase he used in an article in the May 1999 issue of Commentary. In his letter he writes, "There is no evidence that he [Heisenberg] or anyone else in the German project did this calculation correctly during the war," but in fact there is such evidence—in the Farm Hall discussion recorded on the night after Hiroshima, Otto Hahn, one of the ten German scientists, protested Heisenberg's claim that huge amounts of fissionable uranium were required for a bomb. "But tell me why you used to tell me that one needed 50 kilograms of '235' in order to do anything. Now you say one needs two tons." ...
The German physicist Manfred von Ardenne confirms in his memoirs, as he did to me personally in an interview in 1989, that Hahn told him in 1940 that critical mass would be on the order of kilograms, not tons, citing Heisenberg as his source. The fact that Heisenberg had calculated a roughly correct value for critical mass is also demonstrated by his answer to a question during the June 1942 conference in Berlin with Albert Speer. In a letter to Samuel Goudsmit of October 3, 1948, Heisenberg wrote: "General Field Marshall Milch asked me approximately how large a bomb would be, of which the action was sufficient to destroy a large city. I answered at that time, that the bomb, that is the essentially active part, would have been about the size of a pineapple." (Goudsmit papers, American Institute of Physics) The "essentially active part" of a bomb is called the core. Erich Bagge, who was also present at the meeting with Speer, told interviewers, including me, that Heisenberg had shaped his hands in the air to suggest an object about the size of a "football." ...
So there seems to be some residual uncertainty over what Heisenberg knew and when. I guess I'll have to look at the transcripts again, but I distinctly recall Heisenberg being confused about the required critical mass for a bomb. He may very well have worked out the correct figure by his colloquium the following day, but of course that was with the additional knowledge that the Americans had actually produced a working bomb! As all theoreticians know, it's much easier to produce the right calculation once you know the final answer ;-)
An amusing story related by Powers:
... In a letter written to me a few years back the Italian physicist Ugo Fano described a party at the Ann Arbor, Michigan, home of Samuel Goudsmit, scientific director of the Alsos mission, in late August 1939. There two Nobel Prize–winning physicists, Werner Heisenberg, soon to return to Germany, and Enrico Fermi, a refugee from Mussolini's Italy, were both honored guests. "At that party," Fano writes, "[Edoardo] Amaldi drew me aside to point out its humor: 'See Fermi, see Heisenberg, sitting in that corner. Everyone in this room expects a big war and the two of them to lead fission work on opposite sides, but nobody says!'" (Letter of September 18, 1993) Within a month Heisenberg had in effect been drafted to do theoretical work on bomb physics and he soon wrote two papers which were the basis of further German research during the war.