Revealing mistake: When the alien spacecraft crashes into Big Ben, it is obvious that the shot has been reversed/flipped around. Look at the Roman numerals on Big Ben's clock face: They should read (clockwise from the top) XII, I, II, III, and so. Instead they read IIX, IX, X, etc. (00:06:35)
Revealing mistake: In close-ups of the modified pig, seams are visible on its forelimbs. (00:22:45)
Visible crew/equipment: During the warehouse battle, around when the Doctor tells Donna, "Hold on, I'm coming", the film crew can be seen reflected in a door at the right of screen. (00:28:20)
The Day of the Doctor - S7-E16
Clara: Doctor, what's going on?
Eleventh Doctor: It's a... Uh... Timey wimey... Thing.
The Doctor: "Timey" what? "Timey wimey"?
Tenth Doctor: I... I have no idea where he picks that stuff up.
Rise of the Cybermen (1) - S2-E8
Trivia: Only eleven Cybermen costumes were built, but careful filming made it look as if there were more.
Question: 1. Why was Rose not allowed to touch her past self without creating a paradox and causing those creatures to appear and eat everyone, but Amy was allowed to touch her younger self without any repercussions? 2. Why was Rose able to have the time vortex in her head for a few minutes and it only knocked her unconscious whereas the Doctor had it inside him for about 30 seconds and it basically killed him and caused his regeneration?
Chosen answer: 1) When Stephen Moffat took over he ignored a lot of what had been developed before (there is not in-universe answer). 2) It would have killed Rose, so the Doctor absorbed the energy. His body regenerated before the energy could do a significant amount of damage that would prevent regeneration.