I apologize in advance for a long post.
This thread has brought up a number of interesting issues. Germany has always had, since nearly the beginning of the industrial revolution, a remarkable talent for innovation and production. However, for the sake of the original topic, I'll try and limit my comments to issues revolved around warfighting in the ETO during World War II -- in particular, technical, strategic, operational, and tactical issues.
Strategy:
---------
Strategically, Germany did not live up to her potential. The German General Staff tradition influenced every major combatant. In addition to training the bulk of German leadership, most of the finest leaders in the Soviet Army had access to German General Staff training. In fact, the key figure behind the reconstruction of the US Army after the attack at Pearl Harbor had studied in Germany, and used his professional staff training there as a model.
The professional tradition of this General Staff system served German units well at all levels during the conflict, but, with the exception of a number of innovative leaders, most of the Wehrmacht supreme command was bound by limited strategic creativity, whether due to the interference of Hitler's inane directives or their own hidebound traditions. Germany's victory in Poland came at a surprising level of difficulty; the Germans very nearly elected to repeat the disaster of the Schlieffen Plan rather than their attack through the Ardennes during the invasion of France; the choice to engage in Operation Barbarossa was disastrous, and the choice to divert resources away from its successes proved fatal; Rommel's brilliance in the field in North Africa was counterbalanced by tremendous blunders (failure to take Crete when it was possible, continous over-extension of gains) -- the list goes on and on. Oh, and there's the little matter of complete incompetence in the mobilization of industry... Germany's economy didn't even go to a formal wartime footing until 1943.
The Allies, on the other hand, have a better record in this area. The Soviets quickly realized their limitations, knew where to trade land for time and where to stand and fight, and were cynically able to trade massive numbers of men to achieve long-term strategic goals. The British responded to initial disasters in the field with superb focus, maintained air superiority over the Isles to prevent an invasion, and maintained complete sea supremacy, allowing them to continue the fight around the world. The United States recognized the importance of the Europe First strategy, demonstrated a complete mastery of economic mobilization, and worked inexorably to whittle away the gains of the Axis powers.
Tactics:
--------
Despite what some have suggested, the German army set the standard for tactical superiority. German units were trained, even until the end of the war, to maintain cohesion even under stress, and to apply the essentials of fire and movement at all levels. Time and time again, when faced with disaster on a strategic and operational level, German units were able to pull together and stop a total collapse -- accounts are profligate of HQ staffs, engineering units, clerks and typists, and even cooks grabbing weapons and forming firing lines to end overruns by superior forces. And, in nearly every case, German forces were unmatched in mobile warfare. Only elite units among the Allies (Airborne units, Rangers, Marines) matched or exceeded the standard level of tactical excellence amongst the Wehrmacht. Someone asserted that US units had a similar ability to "stick to the mission"... this simply wasn't true in either WWII or Korea, except among exceptional units such as Marines or the Airborne. This deficiency was seen time and time again, from the Kasserine Pass through the Second Battle of the Ardennes Forest (Bulge). Only after these conflicts, when the US military focused heavily on the lessons learned and invested heavily in doctrine and training, was this deficiency addressed.
Operational:
------------
The Germans were the inventors of the term operativ, a word that doesn't translate well into English -- the concept lies somewhere between grand strategy and small-unit tactics, and encompasses the ability of leaders to respond to the unknowable changes and flows in the battlefield.
Ironically, their application of this ability was mixed; some leaders were masters, others less so. The insistence of Hitler and the OKW to interfere on unit-by-unit levels during critical moments of the war overrode any operational abilities held by many leaders -- other masters of the operational art were dismissed by Hitler at various points in the conflict simply for disagreeing with his insanity.
In addition, some crucial Allied forces brought their own levels of expertise here, among them Patton, Bradley, to a lesser extent Montgomery, and many, many of the Soviet leaders from later in the war. Eisenhower showed no great gifts in this arena, as his leadership during Torch shows, but he made up for this in his role as SAC and in his selection of subordinates.
Just as an aside, Robert, most of the examples you quote about beating the best Germany had against odds were not totally accurate. The Rangers were facing horrible odds at Omaha Beach, but they were the finest of the elite of the US military, and the problems were of terrain and firepower -- the German forces on the beaches were primarily second and third-rate units, selected to hold the fortifications due to their lack of mobility, stamina, and-or training. The 101st at Bastogne were, again, an elite unit -- not much more to say about that act of heroism. Patton never commanded Second Army, but rather II Corps, whose successes in North Africa were against high-quality Afrikakorps units that were suffering from extreme deficiencies in supply and total Allied air supremacy. Patton went on to command Third Army, which, again, leveraged his excellent leadership and well-supplied US units with total air supremacy against savavely depleted German units in Operation Cobra.
Technical:
----------
The German army had a mixture of technical innovation and fetishism.
German infantry units used some of the best small-arms of the war, and innovated in ways that still apply today, such as the development of the assault rifle.
German tanks were a mixed bag. Germany's early successes in armored warfare actually came against superior tanks, whether those of the Poles, the French, or British. Leadership, organization, tactics, and communication were the keys to German armored prowess.
The inferiority of German tank design, especially to the Soviet T34, led to the highly vaunted Panther and Tiger series, as well as some truly insane experiments such as the Maus. While Panthers and Tigers outgunned and outarmored the vast majority of their opponents, they faced a serious number of deficiencies. They were insanely complex to develop, build, and maintain. Delays in the development of the Panther delayed Operation Citadel and contributed massively to its subsequent failure at Kursk. These tanks were notoriously unreliable, so nonstandard from tank-to-tank as to make maintenance a nightmare, and desperately vulnerable to combined-arms tactics with infantry (especially in the case of the Tigers). They also lacked mobility, dramatically limiting their utility, and leaving them vulnerable in open battle to more nimble Allied weaponry.
The greatest successes of the Tigers and Panthers were psychological (due to their size, powerful guns, and thick armor), or of limited applicability -- the hedgerows of Normandy balanced the mobility scales and made them kings of the battlefield, but in the open fields and steppes they were quite vulnerable. The Sherman-to-Tiger ratio was primarily skewed by the early static battles in Normandy. In more mobile battles, particularly with upgunned Shermans, they gave a far better accounting of themselves.
(By the way, similarities between the M1 and the Tiger are mainly superficial. Yes, both have dominant guns and incredibly protective front armor. However, the M1 also learned from all the failures of the Tiger... it is extremely mobile, has a reduced profile, is capable against infantry, and is designed for extreme ease of maintenance.)
Shermans were more weakly armored, couldn't penetrate many more advanced tanks with their gun, and caught fire easily, but they were mobile, reliable, maintainable -- a well-balanced infantry tank. The finest tank of the war, from this same perspective of balance, was the above-mentioned T34.
Another quick example: German U-Boats were garbage, especially compared to the submarines of the US. Their threat mainly came from leadership and innovative tactics, but even their strategic threat has been shown post-war to have been exaggerated -- I refer you to the excellent, and definitive, two-part volume "Hitler's U-Boat War" by Clay Blair.
I won't even get into aircraft, mainly because I'm tired. Again, while the Germans showed flashes of brilliance throughout the war, and their pilots were often superb, their aircraft were usually outclassed by Allied planes and their strategic air planning was pathetic.
Conclusion:
-----------
The German military was highly influential both before and after WWII due to innovations in command, leadership, and technology. Many of these areas had extreme deficiencies as well, and in many cases, common beliefs about supposed German or Allied advantages don't hold up to scrutiny.
The war was always unwinnable for Germany, due to a mixture of economic and strategic issues that haven't really even been addressed; it's not fair to say the Allies won simply because of economics, nor is it accurate to say that many standard beliefs about German quality were mythical.