Continuity mistake: When the school bus pulls up to drop Amy and Rory off in Monument Valley, there are no other vehicles in the area. When the bus pulls away, the Doctor has suddenly appeared with a vintage station wagon, parked by the side of the road where it should have been perfectly visible. And he was sitting on the hood, implying he'd been waiting there for a bit. (00:02:45)
Continuity mistake: When the Doctor starts walking over to the lakeshore after the astronaut appears, he's still holding the wine bottle in his right hand. In the next shot where we can see his hand, the bottle is gone, without him having stopped to put it down. (00:06:34)
Continuity mistake: When the Doctor is shot and killed while trying to regenerate on the beach, he falls with both legs extended. When River, Amy and Rory run up to him his left leg is bent. The camera cuts away again, and when it cuts back to show the Doctor's body one more time both legs are straight again. In addition, his left arm changes position between shots, between stretched out pointing away from his body on close-ups to bent with his hand resting on his thigh in wider shots. (00:08:15)
Other mistake: After River shoots at the astronaut going into the lake, she drops her arm. The next second, she turns around and the gun is holstered without her having made any movement to do so, and there was no sound made.
Visible crew/equipment: The astronaut coming out of the lake is seen twice in series 6: In episode 1, "The Impossible Astronaut", and in episode 13, "The Wedding of River Song." In "The Wedding of River Song", when the helmet of the suit is lifted the astronaut is revealed to be River Song. However, in "The Impossible Astronaut", when the helmet was lifted, a man's beard can be seen. Since it is a man in the suit, then it was just a double seen in "The Impossible Astronaut."