Private Caparzo: Captain, the decent thing to do would be take her over to the next town.
Captain John Miller: We're not here to do the decent thing, we're here to follow f*cking orders!
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.
The story James Ryan tells Miller, about his brothers in the barn with Alice Jardin, was not in the script. Matt Damon ad-libbed it and Spielberg decided to leave it in the final film.