Continuity mistake: When Murphy pleads with Cooper to stay shortly before he leaves, as she shows him the message "STAY" on the notebook, in the first shot she looks down, but in the next one she looks at Cooper.
Factual error: The solar panels (or mirrors) are facing away from the sun. The sun's position can be estimated from ground shadows and object highlights and the panels are facing in completely the wrong direction. (01:11:40)