The Doctor, the Widow and the Wardrobe - S7-E1
Factual error: Cyril is introduced looking at the Moon with a telescope... in a brightly-lit room through a window with the curtains mostly shut, circumstances in which he's not going to see anything at all. (00:03:56)
The Wedding of River Song - S6-E14
Factual error: During the zoom-out from Earth at the end, the Sun is depicted as far, far too large than it actually appears from Earth. (00:40:03)
Continuity mistake: When the Doctor finds Joe's corpse, he walks up to him and puts his hand on his shoulder. In the next shot, facing Joe, the Doctor is suddenly in a completely different position relative to him, behind him as opposed to next to him. (00:15:06)
Revealing mistake: The Cyber-Leader has a clear section in the top of its head through which its brain can be seen. The brain in question is very obviously plastic.
Continuity mistake: When Davros activates a screen in the Vault to show the Doctor and Rose the Reality Bomb test, the screen shows the prisoners being herded into the testing area, something that already happened shortly before. (00:23:14)
Factual error: Colonel Mace says the Sontaran ship is orbiting 5,000 miles (8,050 km) above the Earth. However, in shots of and from the ship in both this episode and "The Sontaran Stratagem", the Earth appears far too small for the ship to be that close, with the ship's true distance appearing to be well over double that. (00:08:34)
Continuity mistake: When Rose is telling Auton Mickey that she thinks they should stay away from the Doctor because he's dangerous, a lock of her hair in front of her face tucks itself behind her ear when the shot changes to a close-up. (00:24:42)
Factual error: The upper peninsula of Michigan is missing on the map of the US shown on Van Statten's monitor.
Suggested correction: In that era of Doctor Who the Earth was being invaded by aliens on a regular basis. Since the story is set in the 'future' year of 2012, anything may have happened to wipe that part of Michigan off the map.
I'm from Michigan and when I noticed the UP missing, I jokingly said to a friend "looks like Canada stole that finally"