Continuity mistake: Lamenting his failed SOS call, he retreats to the cabin where he pours himself a drink. After pouring his drink, he puts the bottle down and the bottle is about a third full. As he drinks from the glass, the bottle changes to be more than 1/2 full. (00:23:00)
Visible crew/equipment: Towards the end of the movie, it's night time and Our Man is woken by the sound of an approaching ship. Behind him, in multiple shots, is the moon. If you look closely, extending down and to the right from the moon, you can see the crane/boom arm used to support the studio light used to simulate the "moon." It is visible in the background in several of these shots, but disappears in a wider shot as the scene progresses.
Factual error: As "Our Man" is attempting to repair the radio and other electronics, the radio begins to have intermittent reception. Our Man picks up the microphone and tries to call an "S.O.S." If you look closely, after the third and final attempt, the camera angle changes to an over-the-shoulder shot. Although it's very quick, you can see Robert Redford is holding the microphone backwards, speaking to the "clip" side, not the microphone side.