Continuity mistake: As Lucy goes down the hall, she opens door 214, then 215. As she comes to the next door on the right, she opens 214 again, rather than it being 216. This is particularly noticeable because the third room she enters is "her" room, containing her greatest fear - and the first room she went into numbered 214 had a completely different fear. (00:00:56)
Continuity mistake: When River shows Amy and the Doctor the video of the Angel, next to the Doctor on the ceiling is a bar with two cloth handles, one on each end. The Doctor accidentally rips off the handle closest to him and the viewscreen. A minute later when Amy is alone and we are looking at the Angel video, this handle is back up. It's gone again in subsequent shots.
Factual error: Clara determines the location of the enemy's base of operations: floor 65 of The Shard. However, there are multiple issues with this conclusion. Firstly, floor 65 is a residential property, not an office location; offices in The Shard occupy floors 2 through 28. Secondly, the view of 30 St Mary Axe from Miss Kizlet's window puts the office below 180m, the height of the latter building. This would mean the office must be below floor 50. Finally, when the Doctor rides his motorcycle up the side of the building, 30 St Mary Axe is again seen, this time significantly below his location, and on the wrong side of The Shard. Not only then does the office's height change, but also which side of The Shard it is on. (00:36:06 - 00:38:40)
Continuity mistake: When Martha is searching for how the Daleks changed the design of the Empire State Building, she is examining the plans for the top of the tower. In the first shot where the new plans are visible, the upper right shows a more detailed picture of a plate of Dalekanium. Seconds later, when we can see the new plans again, it's the same side view but the enlarged picture of the plate with the Dalek bumps is gone. These are still the same new plans (the old plans are on her right) and there was no time or reason for Martha to take another page. (00:24:40)
Character mistake: Idris (the human form of the TARDIS) berates the Doctor because the doors of the TARDIS open inwards, pointing to the notice on the left hand door which says 'pull to open'. Whilst it is true that police boxes did open outwards, the notice is actually referring to the telephone in the small recess behind the notice. The public are instructed to 'pull to open' the small door to access the phone. Consequently, the small door does open correctly, as in the notice. (00:23:50)
Factual error: The Doctor meets the future Ada Lovelace in the year 1834, where her maiden name is given as Ada "Gordon." She was actually born Ada Byron, inheriting her last name from her father, the famous author Lord Byron.