On two occasions the cybermen's blue mouth lights are on while the cybermen are not speaking, first when the cybermen are materializing into the chamber and a second time when the doctor is in the Pandorica and its an overhead shot of the alliance.
When The Doctor, Amy, and River first get to Stonehenge, shots of the Doctor alternate between him with a left hair part and using the sonic screwdriver in his right hand and then with a right hair part and using his left hand. That is, the shots are being mirrored.
When River Song is talking to the Romans and they have realized she is not actually Cleopatra, space ships fly over and everything shakes, so visibly that the characters all wobble around as though the ground is vibrating. An ornament hanging from the ceiling, however, fails to move even a fraction, revealing that it is, in fact, just the camera wobbling.
The goof item below may give away important plot points.
Incorrectly regarded as goofs
The Romans did not use saddles with stirrups; they did appear in Europe until the Middle Ages, but, since these Romans are not actual Romans, but creations based on Amy Pond's memories, it's likely the saddles were a mistake made by the Nestene creators rather than any fact given about the time period they were in.