The Short Day of Private Putnam - S2-E28
Revealing mistake: 2/3 through, Beau Bridges comes upon a dead German but you can see the German breathing. Oddly, it's a fairly far shot, so he must have been breathing pretty heavily.
Revealing mistake: When the German soldiers are shot and fall dead into the water, one of them raises his head to take a breath, then goes back to being "dead."
Revealing mistake: In several scenes when they show the front of the barrel of the German machine gun you can see the "blank adaptor" inside the barrel. This is inserted to not allow the gas from the cartridge to escape out the barrel but "blow back" the bolt and insert another round.