Factual error: Miller and his men finally find Ryan in the scene where Ryan destroys a German half track with a bazooka. The camera does not show Ryan firing the bazooka, but you hear the blast and see the effect of the shot hitting the half track, firing twice in about a three second interval. The problem is that a bazooka is a single shot weapon, and must be reloaded by hand. This takes time, perhaps 20 seconds if not more.
Factual error: Captain Miller screams the tank is "still in this fight" and he gets on top of the SdKfz 181 PzKpfw VI Tiger I Tank, and fires his Thompson .45 ACP sub-gun into the view port of the Tiger. Those tanks' viewports were defended by 50-80mm of bulletproof glass and an armoured steel shutter for the driver and commanders cupola. That whole action would have achieved nothing. (02:17:00 - 02:18:00)
Factual error: In the very beginning as the landing craft approaches, and they then begin to disembark, no-one has their helmet chip strap secured. Then attacking the beach, and much throughout the movie, no chip straps. There is no way in real battle you would not secure your lid.