The standard answer you will get from the Internets on this question is along the lines of them not knowing something or not having something. (E.g., Heisenberg couldn't calculate a critical mass correctly, or the Allies sabotaged their heavy water supply, or they didn't realize carbon could be used as a moderator, etc.)

This is essentially a misleading answer. The quick, easy, accurate answer is that the German nuclear program was not an atomic bomb production project. But like many easy answers, it spawns more questions.

One way to think about nuclear weapons programs is that they generally have three stages. The first stage is "exploratory." It means trying to figure out what it would take to build an atomic bomb, e.g. if it is even possible, what you would need to do it, etc. The primary product of such a program is paper — reports, data, equations, formula, graphs, etc.

The second stage is a "pilot" stage. It means trying to build some of the facilities you might need, in small-scale, to see how they work. Its primary product is facilities (but not very big ones) and materials (in very small amounts).

The third stage is a "production" stage. It means trying to actually produce an atomic bomb. This requires the construction of massive facilities, employment of massive labor, and the general expenditure of massive amounts of resources. Its primary product is fissile material and atomic bombs.

So the USA was roughly in an exploratory stage from 1939-1941, a pilot stage in 1942, and a production stage from 1943-1945. In the exploratory stage very little got accomplished except some reports got written and some small experiments got done. In the pilot stage they scaled up some of the experiments and built the world's first nuclear reactor. In the productions stage they built three massive industrial-sized nuclear reactors, several other smaller research reactors, a gaseous diffusion plant, two electromagnetic enrichment plants, a thermal diffusion plant, and actually constructed three atomic bombs.

The Germans never got beyond an exploratory stage, though they did look into building reactors, but never in a big-enough effort to pull it off. They never were confident that atomic bombs could be built during the war, they never spent the resources on getting even the pilot reactors up and running correctly. They certainly got nowhere near a production phase.

One can ask, why didn't they decide bombs could be built? Here is maybe where Heisenberg's misconceptions and other things like that might come in. I think this is sort of the wrong question to ask, though, because it implies that the American approach was the "right" approach. In fact, by 1941 the US scientists had also concluded that an atomic bomb was such a great risk and expenditure that nobody would build one during WWII. They were convinced otherwise by British physicists who were overly optimistic about how easy building an atomic bomb would be. By the time the Americans found out that it was much harder than they thought, they had already invested so much into the project that they just kept pushing it forward to completion.

The original US estimate, that no other power would develop nuclear weapons during WWII, was, in the end, completely accurate. The German and Japanese estimates that it would be so difficult to pull off that nobody else would bother would have been correct, if the Americans had not been misled by the British to think it was easier than it actually was.

So I don't really think the Germans made the "wrong" choice in any objective sense, here. They judged it to be a massive risk and a massive expenditure of resources, and might not work. They were correct. What they judged incorrectly was whether the Americans would be crazy enough to try and do it anyway, and even then, they would have been correct in thinking that unlikely, if not for the British intervention.

Their major error in judgment was that they would not need such a weapon by the end of the war — at the time they made their decisions about atomic research, they were winning. By the time they got desperate enough to wonder if a bomb wouldn't have been useful, it was far too late.