Hitler's biggest mistake.

Which was? Hitler made a lot of big mistakes. He attacked the Russians, who were so terrified of Germany that they were never going to cause him any trouble what so ever. He failed to crush Britain. He ordered his revolutionary jet fighters to be converted into bombers. He refused von Paulus permission to withdraw from Stalingrad. He ordered the fateful counterattack at Mortain, and then refused to allow his generals to withdraw German forces from the Falaise pocket. He abandoned Rommel's army to capture in North Africa. He failed to develop nuclear weapons.
With a list like that, what's left to screw up?
His biggest mistake was to declare war on the United States. He didn't have too. He had no formal or informal agreements with Japan. At the time Germany was locked in mortal combat with the Russians and the British, he didn't need to add to his enemies list.
At the time, the week after Pearl Harbor, the infuriated Americans were about to go after Japan with every thing in the shot locker. Although the American high command and the Roosevelt administration knew that Germany was the more dangerous enemy and they wanted to "Do Germany First", public opinion might have forced a "Do Japan Now" strategy on the administration. Hitler's declaration of war solved that problem for Roosevelt.
With Hitler's declaration of war, Roosevelt was free to do what he wanted to do, namely defeat Germany before flattening Japan.