Audio problem: When the Doctor and Martha are watching Shakespeare in the Globe, Martha says "He's a bit different to his portraits". After she says this on the left of the screen the Doctor's head comes into shot and you can clearly see by his facial expressions he is saying something to Martha, yet no sound is heard.
Continuity mistake: When Yvonne is taking the Doctor and Jackie to the Sphere Room, there is a sign opposite the door that has the words "Torchwood Institute". In the next shot where you can see the corridor from inside the Sphere Chamber, the sign has disappeared. It reappears again when Rose is going into the Sphere Chamber, but this time it has directions to the Reception, Canteen and Lever Room as well as "Torchwood Institute". It also disappears again when you see the corridor from inside the Chamber.