*shrug*
Well, it's kind of hard to argue against Operation Barbarossa being probably the single biggest strategic mistake Hitler made (and he made many of them, very many - so many his own higher officers eventually tried to assasinate him in the interests of the fatherland...). The German military may have been about the best in the world, but it had only so many men and in the end frightfully limited resources and bit more than it could chew. As one German officer is said to have remarked, " before the operation we counted on the enemy being able to mobilize around a hundred divisions. To date we have destroyed over two hundred, and there seems to be no shortage of them" or something along those lines.

In short, the thus far unstoppable German war machine bled itself dry on the steppes through severe underestimation of its enemy (or rather, the German political leadership bled its army dry there but let's not get semantical). The Soviets had the geography on their side and a ridiculously superior manpower pool to draw on, as well as a virtual self-sufficiency on most necessary resources.

Plus their approach to military R&D was rather more sensible than the Germans' "wonder weapons" style. While the latter produced some truly impressive equipement it did so far out of proportion of the industry's ability to manufacture them. It didn't help any that the Germans were pretty bad at the "interchangeable parts" thing. Whereas the Soviets had a bunch of rock-solid grunt designs they kept upgrading through the war the Germans seem to have had an obsession with designing whole new tanks and whatever and then had to convert the assembly lines etc., which wasn't exactly a very effective way to go about it in my opinion. The Americans held the same advantage, for while the Shermans and others were pretty lousy tanks by Soviet and German standards they could be supplied in, for most intents and purposes, endless numbers and more importantly the American industry was completely safe from attack.

Unlike the German one, which famously got bombed to Hell and back whenever possible.

Anyway, I'd say that far more important for the outcome of the war than the oh-so-dramatic D-Day was something rather humdrum and banal - the Lend-Lease scheme. The Soviet tank crews may have considered American lend-lease tanks deathtraps (they gave them nicknames like "a grave for seven brothers"), but US material aid was undoubtly extremely helpful for the Soviets especially during the early part of the war.

By D-Day the Germans were so short on fuel their mechanized unit officers actually had to resort to stealing fuel from each other to get their panzers moving - had Overlord failed Die Reich couldn't have lasted too much longer before collapsing out of sheer and utter shortage of everything (and Stalin had little reason to give them any breaks by that point - the tide had already well and truly turned). Not unlike WW1 really - back then Germany was fairly literally starved into submission.

Though...
Finally, they had landed slap bang on top of a veteran German division recently transferred from the Eastern Front, whereas other beaches had to contend with little more than a few Russian slave labourers.
Really ? Every source I've read stated the best troops the Germans had at the beaches proper were third-rate militias - and the aforementioned East Front POWs in German uniforms (a fair number of whom were volunteers, actually - but then soldiering beats slave labor in a factory). That was really the whole point - the job of such expendable low-quality garrisons was just to buy time with the aid of the fortifications until reinforcements arrived. Or at least this was how Rommel planned it, I understand the guy he shared the command with had another idea (ie. taking the Allies on inland, out of the direct fire support of the ships) and in the end Hitler's bungling kept both of them from doing anything particularly useful.