Unfortunately most of the television dramas based on the German nuclear program take an extremely wide latitude with the facts, in the interest of portraying it as "almost successful" or acting as if there had actually been a "race for the bomb." In reality the German program was very modest and was nowhere near getting a bomb, and would not have achieved a bomb even if there had not been sabotage. But that makes for poor television.

Heisenberg ran one of the research groups that looked at nuclear fission issues. The German program was not a weapon-production program; it was a reactor research program from 1942 onward.

The German programs changed in organization several times over the course of the war, but here's a basic org chart for early 1942, when it was split into six different institutes each under a different head:

• 1 Walter Bothe (Heidelberg): six physicists; measurements of nuclear constants
• 2 Klaus Clusius (Munich): around four physical chemists and physicists; isotope separation and heavy water production
• 3 Kurt Diebner (Army Ordnance lab in Berlin-Gottow): around five physicists; measurements of nuclear constants
• 4 Otto Hahn (Berlin-Dahlem): around six chemists and physicists transuranic elements, fission products, isotope separation, measurements of nuclear constants
• 5 Paul Harteck (Hamburg): five physical chemists, physicists, and chemists; heavy water production and isotope separation
• 6 Werner Heisenberg (Berlin-Dahlem as advisor; Leipzig): around seven physicists and physical chemists; uranium machines, isotope separation, and measurements of nuclear constants
• 7 Hans Kopfermann (Kiel, later Gottingen): two physicists; isotope separation
• 8 Nikolaus Riehl (Berlin, Auer Company): around three researchers, although the larger reserves of the firm could be drawn upon; uranium production
• 9 Georg Stetter (Vienna); around six physicists and physical chemists; measurements of nuclear constants and transuranic elements (quoted from Walker, 52-53)

As you can see, Heisenberg in this approach is just one of several people working on the issue, with an extremely modest technical staff size. His topic, "uranium machines," is what they called nuclear reactors at the time in Germany. So it was an important part of the program, but not the entire program. Ultimately there would be two research groups working on "uranium machines" (the other headed by Diebner). Neither achieved success during the war. Heisenberg was certainly an important scientist on the project, and the most imminent physicist working on it by a considerable degree. But he was not leading a bomb effort. He was leading a reactor effort. There is a difference.

I haven't seen the show so I can't comment on the scene. I suspect it is based on the fact that, in the Farm Hall transcripts from after the war, Heisenberg gave radically incorrect numbers initially for how much fuel you would need for a bomb, basically confusing the physics with that of a nuclear reactor. He later revised this. This is sometimes pointed to as the "reason" that the Germans never really pursued a bomb — that this one simple calculation somehow led them to think it was impossible. In reality, again, there were many people working on the project. When the Germans decided not to invest heavily in building a nuclear bomb, they had a reasonably good estimate of how much fuel was necessary in front of them: between 10 and 100 kg of enriched uranium ought to do the trick, they understood in December 1941 (Walker, 48). This is a correct order of magnitude estimate (the real answer is around 50 kg for a bare sphere critical mass). They decided, arguably correctly, that this was still too much work to imagine investing in given the other pressures on them.

For a very detailed and sober discussion of the German atomic program, without any of the false drama cooked up for television, see Mark Walker, German National Socialism and the Quest for Nuclear Power, 1939-1949 (Cambridge University Press, 1989).