Factual errors: A few snippets of dialogue in the scenes in the East German university clearly show that the extras are Americans.
Boom mic visible: Reflected in the window of the farmhouse as Armstrong enters.
Crew or equipment visible: Or their shadow, anyway. On the road-level shot of Armstrong's taxi leaving the farm (Gromek's motorbike is visible on the left of the screen), just at the very bottom of the image can be seen the shadow of the camera (4:3 television version only).
Revealing mistakes: In the farmhouse scene when Professor Armstrong is fighting with Gromek, Gromek is choking Professor Armstrong but Armstrong shows no signs of it, i.e. bruising, in later scenes.
Factual errors: When Professor Michael Armstrong (Paul Newman) is writing the address on a piece of paper in the beginning of the movie he writes: Kobenavn. The actual spelling is: Kobenhavn.
Revealing mistakes: When Professor Armstrong is on the boat, the heater aboard ship is broken, and the close-up of the thermometer shows it is freezing - yet it spite of the fact that he and all the extras are wearing heavy coats, their breath yields no steam, which would have been profuse at that temperature.
Revealing mistakes: The handwriting Professor Armstrong gives to the radio operator aboard ship and the note that he later writes to his fiancée is not the same - both handwriting samples clearly do not match.