Continuity: When they go to find Private Ryan there are eight of them, when they go to a French town and a solider picks up the little girl and he gets killed there are seven, right? Wrong. A few scenes later, the camera shows all eight of them marching on to the next town, only in a far away camera shot so it's hard to see.
Captain Miller: He better be worth it. He better go home and cure a disease, or invent a longer-lasting light bulb.
In the closing battle of the film we see one of the American soldiers with an ammunition belt around his neck. The striker marks on the primers indicate that the belt is made up of fired (ie. useless) cases which have had bullets put back into them so they look normal. See more...
The resentment the soldiers feel towards Pvt. Ryan is real: Matt Damon was the only cast member who didn't go through boot camp. See more...
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Continuity: In the scene in the Pentagon between several officers and General Marshall, when the camera pans over Marshall's left shoulder towards the officers, you can see that the colonel, who was missing his left arm in earlier scenes, has it again; it's missing again in the next shot. It may be just that his sleeve's rolled down in the middle shot, but that's still an error.
Revealing: Just before the two American soldiers slap their grease coated "sticky bombs" on the passing German Tiger tank, you can clearly see two identically shaped grease stains on the first two wheels. Presumably nobody remembered to wipe off the wheels of the tank after a rehearsal or previous take of the scene.
The majority of the extras in the movie were from the Irish Army and the F.C.A. (a military organisation). Direct from one of these extras: in the opening scenes where the soldiers are in the boats before landing at the French beach against German defenders, the soldiers puke their guts out, and we all see this. What you don't know is that it was REAL vomit you see - it was caught on camera perfectly and it was kept.
There is a very common misconception that the guy that they let go at the radar station, who ends up shooting the captain, is the same actor/character as the guy that stabs and kills Mellish. It's understandable because they do actually look very similar, but if you look closely you'll see that they are, in deed, not played by the same actors. The guy with the knife is not quite as bald, doesn't have two wounds under his right eye, and has connected earlobes. The one that they let go and later shoots the caption is more bald, has the two wounds under his eye, and does not have connected earlobes. Plus their mannerisms and voices are very different.