When Clara goes to the TARDIS, she is not wearing her jacket. Later she has it on.
The Doctor should remember that Clara, as the "Impossible Girl," was present in every moment of the Doctor's life to save him, and not allow the TARDIS extrapolate her time line when it includes all of his as well. But this Doctor has demonstrated other memory loss in series 8, possibly because he is the first regeneration in a new set (of 12) and the consequences of that are not fully known.
After writing on his blackboards the Doctor places a piece of chalk on to a book. When he picks it up after it (supposedly) falls to the floor the chalk stick shows no sign of use.
The time ship that Orson Pink was in was designed for a solo time trip yet it has two seats.