When The Doctor is working in the TARDIS, there's a table full of things. After The Doctor, Clara, and Danny leave, Courtney looks in and the table is gone.
As Clara and the Doctor tell Danny about the the TARDIS a stack of plastic chairs continues to burn with visible flame and copious amounts of smoke. This should set off the smoke detectors and trip a fire alarm, yet no alarm is heard.
At the very end of the episode, the cop killed at the start is being interview in the afterlife. When he realizes he did not get out of that tight spot he looks out the window through the blinds. A stripe of light is seen across his lower face but his eyes are in shadow. If he were really peeking out of the blinds the stripe of light would fall across his eye, not his mouth.