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.
All Is Lost (2013)
1 factual error - chronological order
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)