Revealing mistake: Mels is shot in the stomach by Hitler, leading to her regeneration. Rory, when checking the wound, says he's going to try and stop the bleeding. However, when she stands up while glowing with regeneration energy, and in every scene afterwards where Mels/River is wearing that dress, there is no bullet hole or bloodstain visible.
The Impossible Astronaut - S6-E2
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.
Suggested correction: The holster is low enough for the subtle movement her right arm makes to be using it. As for the sound, the removal of her gun doesn't make a sound either. The only sound heard is directly before it when she put her medical scanner away.
The Impossible Astronaut - S6-E2
Visible crew/equipment: The astronaut coming out of the lake is 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. Clearly the use of a double to avoid giving the reveal away too early.