A character in one scene has two shadows, while the rest have only one. In wide overhead shots, he has two shadows, but in tighter shots from floor level, he has only one shadow.
Moments after the first anomalous shadow is noticed to have disappeared but before the expedition team arrives, the security camera The Doctor had been inspecting on the floor in the center of the room disappears.
At the beginning the door to the library is being rattled quite violently but when The Doctor and Donna enter in flashback, they are not trying to rattle the door: The Doctor uses his sonic screwdriver and Donna kicks it once.
When The Doctor and Donna are running down the corridor with the lights that are switching off, and Donna kicks open the door, you can plainly see that when they relax, there is still a crack of light coming through the door, indicating that there was no need to run in the first place.
When River is using the neural link to ask Ms. Evangelista her position, River stops holding the button on her end for the last two words ("your position") but the echo effect, caused by Ms. Evangelista's link being nearby, is still heard.
When the swarm begins walking around in the EVA suit you can clearly see that the neural link has lost power, yet you can still hear the previous occupants voice 'ghosting'.
When the phone rings and the girl stands up, the mic is visible above her father and Dr. Moon.
River's later appearances in the series lead to a continuity error because she questions the Tenth Doctor about the crash of the Byzantium, an adventure she shared with the Eleventh Doctor. This makes sense if she is mistaking the Tenth Doctor for a Twelfth or later incarnation, but in The Husbands of River Song (2015), which takes place immediately prior to this story from River's point of view, she is shown to have a complete collection of the Doctor's faces in proper chronological order.
The Doctor repeatedly tells everyone to stay out of the shadows, not let their shadows touch, etc., yet people repeatedly stand in shadow and work in close proximity. Even the Doctor himself runs in and out of darkened spaces just moving around the little shop.