Plot hole: Azmael doesn't recognise the regenerated Doctor (In the shape of Colin Baker) whereas on most other occasions other Time Lords do recognize each other through telepathy. This is odd behaviour by Azmael, considering that Azmael and the Doctor HAVE actually met before, and possibly more than once. (Azmael last met the Doctor in the Doctor's fourth incarnation, and was the best teacher the Doctor ever had. On that occasion, Azmael got drunk.).
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.
Continuity mistake: When the twins start to play equations they are both facing towards us. If they were to face each other, their legs would be touching each other. During the game we again see them at this distance apart. But the third time we see them (as they finish), they have moved at least a metre apart, making it possible for them to face each other comfortably.