Plot hole: When Della gets shot in the face in episode four, she clutches her stomach. (What is even more remarkable about this error is that this keeps happening over and over again: someone gets shot and falls to the ground, clutching their stomachs, regardless of where they have actually been shot. See the error in Season 14's 'The Deadly Assassin' for an example of the SAME error occurring).
Continuity mistake: The use of gold against the Cybermen is wildly inconsistent in this episode. It is said that it suffocates them. Yet Cyberman have been seen functioning perfectly in vacuum ("The Moonbase" and "The Wheel in Space"), it affects the Cybermats, who are little more than metal drones, and it affects the Cybermen's radar, which does not breathe.
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: In episode 3, when the Doctor leaves the old house to find the dynamite, you can see his hat resting on a chair as he walks out the door. Immediately afterwards you see him walking through the woods with Sarah, and see that the hat has magically relocated itself to being back on his head again. And when he eventually gets back to the cottage, the hat is there, still in the chair as if nothing had happened.
Plot hole: The junkyard at 76 Totters Lane seen in "Attack of the Cybermen" was also in "An Unearthly Child", the very first episode of the show. If you consider London's high land value, it is highly unlikely that an ownerless junkyard would still survive twenty-two years... the local authority would have long since issued a "compulsory purchase order".
Revealing mistake: Watch Elena's monitor screen just before she taps some keys and gets the display of information about the XV773 freighter. It's filled with a mass of tiny text which initially looks like just gibberish but if you look closer, you'll see it's actually the computer program used to create the information display. Someone has even typed in the RUN command at the bottom of the screen, so that all the actress had to do was press the ENTER key and an instant faked "information readout" appears.