How close were the Nazis to winning World War 2?

I had a history professor in college who once said by late 41 Germany had almost won the war. It was now for Germany to win or lose, not for the Allies to win. Germany had the strategic initiative, she had the power and the training and the esprit de corps of the troops after winning virtually none stop. The myth of Nazi invincibility was very much evident in Europe during those days. It appeared that there was nothing the Germans could not conquer. At this time, Hitler began making mistakes that Germany could not compensate for. Several of these are well known. First was not going thru and taking Dunkirk. Over 330,000 allied troops were evacuated. True they left all of their heavy equipment, but if the Wehrmacht had seized Dunkirk, then Britain would have been open for an invasion. The next big miss for the Germans was their U-boat effort. Doenitz stated that with 300 U-boats he could choke Britain into submission. The point he was never able to make on Hitler was with boats returning from patrol and others going out onto patrol, that the total number you had actually involved in sinking transports was 1/3. If more emphasis had been placed upon the U-boat arm, then things could have been different. Remember Churchill said the only thing that ever worried him during the war was the U-boat menace. The next big wasted chance was during Aug. 41 when army group Center stood ready to drive on Moscow. Besides the capital and the hub of all rail roads in European Russia, Stalin's prestige would have been seriously damaged if the Germans took Moscow. Instead, Hitler diverted the panzers south to Kiev. Then they turned around and drove north, right back to where they had started from. And the last major nail in the Axis' coffin was the German declaration of war upon the US. Without this, it would have been very difficult if not impossible for FDR to have declared war upon Germany. The US was outraged at the bombing of Pearl, so they would have turned to the Pacific and dealt the Japanese a very sore hurting.