Revealing mistake: Whenever there's a close-up of Davros, it's very easy to see that there's a gap around his mouth where the mask should blend in with the actor's face, but doesn't. This mistake was rectified, incidentally, in Davros' next appearance in "Destiny of the Daleks."
Plot hole: Peri goes to a fair bit of trouble to bolt the door on the bath house when rescuing the Doctor. When the Rani and the Master arrive, they simply open the door. Now this, in itself, isn't a mistake, as the Master has a special gadget for opening locked/bolted doors, but both the Master and the Rani seem surprised that someone is in the bath house.
Revealing mistake: At various times (especially in episodes 3 and 4) you can see actor Stephen Thorne's lips through Omega's mask (and in one profile shot you can also see his jaw), yet when his mask is removed, we find that Omega has been dissipated and has no face...