The main cause of German failure can be traced directly back to Hitler. Hitler felt that Germany lost WWI because of collapse back home (the famous "Stab in the back."). This caused him to seek a better way of fighting than those of the Great War. The "Blitzkrieg" seemed to offer that better way. Unfortunatly for Hitler (and fortunatly for the rest of us) the concept of lighting war became not only military but political doctrine as well.
The German economy was not mobilized till about the middle of '42. Nearly all research into strategic programs was discontinued (heavy bombers being the most obvious) as unnecessary. Conquered nations were to by looted for usable supplies and then governed as Germany saw fit. This all translated into a Wehrmacht that was high powered but short ranged. It was the only one of the major powers to rely as heavily as it did on horses for transport. For all its percieved technological prowes it was in actuallity the most backwards of all the armies from an overall point of view. While it had some standout weapons, most of its systems were inferior to their allied counterparts. German troops prefered the superiour Russian submachineguns and came nowhere near matching the Russian cold weather equipment. German radar was so inferior to British and American sets that the Germans underestimated the capabilities of the Allied units for the entire war. The American M1 Garand was the best rifle of the war and the Germans were amazed by our field radios. Most important of all the Germans never designed an easily manufactured gp truck to compare with the American duce and a half. It was these trucks that carried the Allied armies and all their supplies to victory. Conversly it was the lack of them that not only hampered but destroyed any hope that the Germans had of supplying their invading armies. This lack of motor transport effected the German war effort at all levels by depriving troops of mobility (during the Battle of the Bulge, 2 Panzer was forced to mount one of its PzGren Bns on bikes because of lack of transport) and depriving its armies of supplies. This lack came directly from Hitler's unwillingness to mobilized the country behind the war effort.
As to the Germans learning from the Russians you have to look at the track record. Up until Kursk the Russians had never stopped the Germans from achieving a breakthrough into the operational zone. In other words, while they had stopped them from siezing the strategic objectives (Leningrad, Moscow, etc...) the Germans had always broken through the initial Soviet lines. This gave the Germans little incentive to change their methodes. After Kursk they lacked the power to launch anymore massive offensives and so again there was no opportunity to change their methodes.
In the end it was only the size of the Soviet Union that saved it from defeat. If the Soviet capital were Minsk or Kiev the Soviets would have been defeated. As it was they had kind of a natural defense in depth as it took so long for the Germans to get to their objectives that the Soviets could afford to make dissasterous mistakes without capitulating. The limits of the Soviet command structure and training prevented any true mirroring of German tactics but their ability to turn their entire manufacturing base to the production of weaponry (because we were making all their other supplies) insured that they could quickly build up massive numbers needed to be successful at what they did learn from the Germans. No one ever called Soviet tactics subtle but they were very effective.
One last thing. In the discussions of the developement of armored tactics one should look up the contributions of General Percy Hobart. His work, while largely ignored by his own government in Britan, was very influencial in Germany. Gudarian claimed to be greatly influenced by Hobart's theories. You may know Hobart best as the commander of the British 79th Armored Division better known as "Hobart's Funnies." Also about the tactical use of Airborne troops, I think Salerno was about as close as you can get to a tactical drop.