Other mistake: During the Omaha Beach scene, the radio man lying next to Tom Hanks suffers a massive wound to his face, killing him. But there is no blood or gore at all, just a hole in his face. It is impossible to sustain this type of injury and have no blood present.
Factual error: When Jackson takes out the German sniper, we see the German snipers point of view through his scope and he eventually spots Jackson who fires at him. First you see the flash, then the bang, and then the German sniper gets hit through his scope. This is wrong because bullets from a powerful sniper rifle travel much faster than sound, he couldn't have heard the shot before he got hit. (00:51:30)
Stupidity: When they are preparing for a German assault towards the end of the movie, Miller explains to them the concept of the sticky bomb and adds, "If you have a better idea of knocking the treads off a tank I'd like to hear it." Um... The bazooka? They had eight rounds for it, and it could have easily been used to disable the treads. And the men wouldn't blow themselves up with it. While it couldn't destroy a tank by penetrating the armour, it's certainly strong enough to disable the tracks.