Continuity mistake: At many points in this story there are problems with the costume that Zoe is wearing...the zip is often jammed part or all the way open. Not only does this leave most of her back exposed, but the position of the zip tends to change position during scenes, as while off camera Zoe tries to pull the zip back up, only for it to open up again minutes later. (It is a little unkind to say it, but possibly the costume was a little bit too tight for Zoe, causing it 'self unzip'?).
Revealing mistake: The Cyberman that falls from the roof in the final episode is obviously an empty costume. (This is another example of a mistake being repeated from an earlier episode. See the earlier story "The Tomb of the Cybermen" for a note about the same 'revealing' mistake happening).
Continuity mistake: Near the end of episode three, Jamie starts to read the printout. At first, he is reading the printout the right way round. But when we next see him, he seems to be reading it upside down. Then the third time we see him, he is back to reading it correctly (right way up).
Continuity mistake: When the TARDIS breaks apart and the console sent spinning off into space, Zoe is lying on it. In close-ups she lying on her left side facing towards Jamie (who is opposite), but in the distance shots done with small models, she is lying on her right side facing away from Jamie.
Continuity mistake: After the second doctor's regeneration, the TARDIS lands in a field with trees around it. When the third doctor comes out of the TARDIS, the background changes completely.