Would it really be worth making the recruits' crappy weapons less accurate anyway? I mean, yeah they might be less accurate if they are worn and dirty, but at most the recruits will have a what, 1% degradation in accuracy? The bullet is still gonna have to go wherever the barrel is pointing. It isn't like the recruits will have smoothbores and the heroes will all get issued sniper-grade weapons.
Actually, the people who were first sent to the front, on the German side at least, would probably have the best weapons because they would have been manufactured during peace time. Matter of fact it was probably by the end of Stalingrad that the Germans had had all their best trained and best equipped troops starved to death. It was the Volksgrenadiers on the final days of the front that probably had the worst equipment.
Granted, I'm sure if you're a friggin' Knight's Cross or something you got the latest and greatest, but it's worth considering that wartime versus peacetime manufacture sees significant degradation, particularly in finish.
From what I've read, also, there is significant variation in wartime firearms for that very reason in terms of accuracy. I've read some people on boards (not exactly premium information, but you get the idea) saying their Lee Enfields, M44s, etc, vary in accuracy from 2-4 MOA. This, keeping in mind that this is wartime surplus and that all of them have been around for decades under who knows what conditions and have all had some kind of corrosive ammunition fired from them. But suffice to say, yes, accuracy was variable, as I understand it.
I also want to say that it's probable NOBODY carrying a Mosin Nagant or particularly the Kar98 had to worry about jams. Mauser is reputed to be an impossibly reliable extraction system.
I'm sure this must have been an issue with some of the speedily constructed submachine guns, though, and obviously jams would be rampant with G41 under battlefield conditions (high tolerances, very finnicky mechanism).