Revealing mistake: During the battle of Ramelle, when two men of the 101st prepare to firebomb a Marder tank destroyer from above, one of its German crew is looking up, spotting them. For that instant, you can see the pasty fireproof mask covering the German's face. (02:15:34)
Other mistake: When Melish is stabbed by the German soldier, Melish's body isn't consistent with the floor. It's almost as if he his lying underneath the floor.
Revealing mistake: The shot of the eight members of the group is reused later in the film when there should only be seven.
Suggested correction: This is much too vague. Where is the repeated shot used?
Continuity mistake: Sunlight changes from shot to shot during the machine gun nest scene. One second it's like cloudy, in the next you see the sunshine and long shadows.
Factual error: Near the end of the movie when an American fighter saves the day, it's a P-51 Mustang. In June, 1944 the most likely ground support fighter would have been the P-47 Thunderbolt. Also, American planes were still painted olive drab at that point. The Mustang in the movie did have black and white invasion stripes, but it's the wrong plane and the wrong color.
Suggested correction: The P-51 was one of the most commonly used fighter planes in the USAF by mid-1944. These planes had been flying in Europe since 1942, starting with the RAF, its original user. There are colored pictures of Mustangs with the paint job depicted in the movie from mid-1944 as well.
Continuity mistake: During the final battle, they stop the tank in its tracks and several approach it. Captain Miller runs up with them. He is about to start shooting into the view finder but doesn't. The scene cuts and the tank shoots at the area where Ryan and Reiben are. Cut back to the tank and Captain Miller is still standing next to the tank, and he shoots in the view window, repeating the action from the previous shot.
Continuity mistake: Right before Capazzo dies he holds up the letter, but it's in a zip-lock bag. After the sniper is killed the medic retrieves the soaking wet, unbagged letter.
Suggested correction: The letter is never in any bag, plastic or otherwise. It's always bare or else he wouldn't be worried if there is blood on it. Zip-lock bags weren't invented until the 1950's anyway.