When Christina enters Captain Lancasters office, the captains feet are on the desk, in the next shot, he removes his feet from the desk and sits up straight, then it returns to the original view and his feet are still on the desk.
Human skulls cannot float on water, as human bone is denser than both fresh and salt water.
The entrance to Titus' vault is revealed by moonlight reflecting off of the statue, then off of a parchment in a wall case and onto the correct section pushed to open the door. However, Titus died in 1833, over a hundred years earlier. There is no way that the displays in the museum have remained untouched for that long.