Continuity mistake: At the beginning, when the Doctor takes Amy to planet One, he holds out his hand for Amy to take hold of when they're about to leave the TARDIS. When you see her from the back, Amy lifts her hand wearing her red fingerless gloves. But when it switches shot and faces Amy from the front, she takes the Doctor's hand wearing no gloves. When she steps out of the TARDIS, her gloves are on again.
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)
Continuity mistake: Near the end, when the Doctor is explaining to Amy that she will forget Rory when the crack in time is finished eating him because he's part of her personal timeline, and he has his hands on her temples, Amy's hair is covering her ears in some shots, but not others.
Continuity mistake: When River is talking to the Roman commander after disintegrating a piece of furniture with her pistol, she is shown raising her fingers from the pistol's grip in a shot facing the commander. However, in all following shots facing her, her fingers are still lowered.