Hitler’s, and the Axis’s, biggest overall mistake was the failure to identify, agree upon, and relentlessly pursue a common Axis aim, which is the exact opposite of the Allied position, regardless of the disputes and suspicions which may have plagued the Allies. This allowed each of the three major Axis powers to go off on exercises of their own without regard to the overall Axis position, and frequently in a way highly damaging to it and other members.
While attacking the USSR may have been Hitler’s biggest military mistake, it was made far worse by his betrayal of Japan in doing so, which altered Japan’s grand strategy in a way fatal to Hitler’s chances of achieving his grand strategy aim with the USSR.
In 1941 there were vigorous debates in Japanese strategy formulation circles about whether to attack northwards into Russia or southwards into SE Asia etc.
One of the significant factors for opponents of the northwards attack was Hitler’s betrayal of one of the major and supposedly agreed common aims of the Axis powers contained in the 1936-37 Anti-Comintern Pact http://www.yale.edu/lawweb/avalon/wwii/tri1.htm http://www.yale.edu/lawweb/avalon/wwii/tri2.htm http://www.yale.edu/lawweb/avalon/wwii/tri3.htm
The intent of that pact was to contain the USSR and prevent the spread of communism. While not explicitly saying so, it saw the USSR as the enemy of all three signatories.
When Germany signed the Non-Aggression Treaty with the USSR http://www.yale.edu/lawweb/avalon/nazsov/nonagres.htm in August 1939, without Germany forewarning Japan or seeking its agreement and while Japan was fighting a major campaign against the USSR at Nomonhan, the treaty was perceived by many in Japan as a betrayal of Japan by Germany.
When the position was reversed after Germany attacked the USSR in mid-1941, and bearing in mind that Article 3 of the Tri-Partite Pact http://www.yale.edu/lawweb/avalon/wwii/triparti.htm required the other parties to come to a signatory’s aid only if attacked by another nation, there was strong opposition in some quarters in Japan to aid Germany by attacking Russia. The reluctance was reinforced by the fact that Hitler attacked the USSR while the non-aggression treaty between them was in force, which increased Japanese distrust of him. Other factors, unrelated to Hitler’s actions, were that Japan assessed the risk of a Soviet attack against it as low and saw no point in antagonizing a sleeping dog, and resource and other issues dictated that a southward advance served Japan’s interests much better.
Had Hitler not been so treacherous towards Japan as an ally, and towards the USSR under the non-aggression treaty, he might well have been able to capitalise on the strong support for an attack into the USSR by Japan in 1941, so that Japan’s forces would have been devoted entirely to such an attack when the USSR was at its most vulnerable.
This would have meant that there was no southwards advance by Japan and no Pearl Harbor etc, at least not for another two to three years, if ever. America probably would not have come into the war against all, or any, Axis powers if Japan did not attack it. Hitler might well have won in Europe and the western USSR, with the USSR being carved up between Germany and Japan.
In the end, so far as attacking the USSR was concerned, Hitler’s first and biggest mistake was being as treacherous towards his allies and treaty partners as he was towards his acknowledged enemies. But for that, his military strategies might have succeeded.