The spy hole on the cell door is the wrong way around to keep watch on the prisoner, the prisoner would be able to see his guard far better.
The Doctor makes a reel of tape he is holding vanish into thin air, then makes it reappear a few moments later. No explanation is given for this magic act, other than some vague technobabble. If the Doctor was capable of performing feats of magic like this, why has he never done it before or since.