Continuity mistake: After Miss Evangelista is killed, we see her communicator as her "ghost" slowly fades. In one shot we see from a slight distance the lights left lit tick down to 3, then a short while passes, we cut back and the lights are back to 4. They then tick down to 3 again.
Revealing mistake: When the Doctor notices the unnatural triangular shadow signalling the presence of the Vashta Nerada and points it out to Donna, the shadow appears over Donna when she's standing in front of it, showing that it's a special effect added to the shot afterwards. (00:11:10)
Visible crew/equipment: While the Doctor tries to get into the data core (after Proper Dave tried) it cuts to the telephone still ringing, and when the young girl asks her dad why he's not answering the phone, just as he tells her that the phone is not ringing the boom mic dips into view at the top of the screen. (00:19:40)