Was Hitler's biggest mistake driving out German scientists that had a Jewish background?
It is difficult to say that Hitler's biggest mistake was to do this when he made so many other mistakes.
Morally speaking, the Holocaust is by far and away Hitler's biggest mistake. It was one of the most unspeakable acts in all of human history.
If you are simply talking about mistakes that cost Hitler the war, then I would argue that the invasion of Russia was much worse of a mistake than driving out the Jewish scientists. If Hitler had not invaded Russia, it is not at all likely that that he would have lost his gains in Western Europe. If the whole German army had been free to act in Western Europe, it is hard to imagine the Allies even trying to invade the continent. We have to remember how badly the Eastern Front hurt Germany and how much easier that made the job of defeating Germany in the West.
I would argue then, that the invasion of Russia was Hitler's biggest strategic mistake and the main cause of Germany's defeat in WWII.