War on two fronts is always a bad thing. It divides your forces, complicates supply, and generally leaves your enemy with a large advantage. Hitler's impatience in attacking Russia before subduing Britain effectively cost Germany the war.

Never underestimate the power of numbers. Germany relied far too heavily on it's technical superiority, which wasn't even always there! Sherman tanks may have been easy meat for the Tigers and Panthers, but they were reliable and very easy to churn out in their thousands - Germany didn't tool up early enough for "total war".

Never underestimate the power of logistics. The best aircraft and tanks in the world are worth nothing if you have no fuel or ammunition for them. This seemed to be almost completely overlooked by some of the German high command in their battle plans, an absolutely fatal error. An army must have proper supply routes.

A battle is won by tactical thinking, not emotional response. Hitler often gave orders which were quite plainly driven by emotions rather than their merit in the overall tactical plan. This was a complete waste of resources which detracted from the main objectives at the time. Focus is very important! He thought of himself as the best military strategist ever, often rejecting the advice of those far better qualified.

Knowledge is power. The attack on Russia at the Kursk salient was one of the largest single military maneuvers of all time, and it should have decimated the defences. The Russians, however, learned of the attack and prepared a trap which resulted in the largest tank battle of all time and crippled the German offensive and ripping the heart from the feared Panzer divisions.

False knowledge is death. Goering told Hitler his Luftwaffe could supply the stranded troops at Stalingrad by air (yeah, right!). He couldn't, and they were destroyed. Make sure that intelligence you are making important decisions on is accurate or you may find yourself over- or under- committed.