Factual error: After the birth of the baby, James Stewart and "Doc" Witherspoon are discussing the course of the war. "Doc" relates that he has always lived in Virginia and that his son died at Gettysburg at Little Round Top. No Virginia regiments fought at Little Round Top - only Alabama, Texas, Georgia, and Arkansas regiments.
Factual error: None of the German tanks are accurate representations of German WWII types. They are all post war US variants. ie. M47 Patton Tanks. [Still a mistake, but an elaboration: This is a common problem in depicting German tanks: few, if any, survived the war. The few museum examples wouldn't be released for movie work, and certainly WHERE, some 20 years after the war, would one find a brigade's worth of running Tiger II tanks? Never mind that Kampgruppe Pieper, which Hessler's command is loosely based on, actually used Mark IV and Panther tanks. There was one King Tiger battalion, and it was in reserve well behind KG Peiper. The M47s versus the M24 Chafees (mistakenly called "Shermans" at times) is a fairly accurate comparison of the respective sizes, firepower, and other combat capabilities of the respective tanks. Some other movies, like "Kelly's Heroes", have their "Tigers" mocked-up with sheet metal, wire mesh, and sacking over a different type of tank (in that case, T-34/85s of the Yugoslav army are mocked up as Tiger Is, a fairly decent job).]
Continuity mistake: When they are all lined up for their medical inspection at the beginning of the film, the sun is coming up behind the hut casting a shadow in the front. When the Sargeant Major is then shown shouting from the hut, "I want this one (Bartlet) scrubbed with a yard broom." You can now see by the shadows that the sun is shinning directly at the hut. This would be impossible as there is only a few seconds between shots for this change to happen.
Continuity mistake: The city railroad scenes were filmed in Spain, and many of the forest railroad scenes were filmed in Finland; in both of those countries, most of the railroad track is broad gauge (the rails are more than 5 feet apart). The plains and mountains railroad scenes were largely shot in Canada, where the rails are "standard gauge": 4' 8 & 1/2" apart. The rails can be seen to jump between far apart and closer together more than once as the movie progresses.
Revealing mistake: In the opening sequence when Colonel Ryan's plane has crashed and is on fire, you can see a metal pole supporting a burning aircraft shell, not a real plane.
Factual error: In a wide shot of a battle, pictured in the background is a cooling tower for a nuclear plant. These did not exist during this time period.
Continuity mistake: James Garner figures out he's being duped, and tells Eva Marie Saint to run out of the room screaming to draw attention to herself. She does and there's a shot of her on the hospital lawn with staff all around her. The next shot is James Garner looking out the window to see what their reaction is, and Eva Marie Saint can be seen behind him in the room.