Continuity mistake: When River shows Amy and the Doctor the video of the Angel, next to the Doctor on the ceiling is a bar with two cloth handles, one on each end. The Doctor accidentally rips off the handle closest to him and the viewscreen. A minute later when Amy is alone and we are looking at the Angel video, this handle is back up. It's gone again in subsequent shots.
Continuity mistake: When the Doctor and Amy are in the museum looking at the Home Box, after they steal it, they run to and enter the TARDIS, which is parked at the end of the hall by the last glass case. However, in the first shots of them in the museum, the camera was pointed directly at that spot, and the TARDIS wasn't there. (00:02:20 - 00:03:00)