The box containing the Scroll of Life is very similar to a box that was found in Tutankhamun's tomb, and indeed bears his name in hieroglyphs. They say Ananka has been dead for 4000 years. 1898 - 4000 = 2103 BC (there being no year 0). Tutankhamun was born around 1343 BC. It does not make sense for his name to be on a box in her tomb.
Princess Ananka's mummy's death mask has closed eyes. In reality, the eyes of an ancient Egyptian mummy mask are wide open because the Egyptians wanted their dead to be able to see and hear in the afterlife.
When the mummy - supposedly wrapped in ancient strips of cloth from thousands of years ago - breaks into the padded cell at the asylum and kills Stephen Banning, after he finishes the murder, he turns around revealing a clear seam in the costume were the zipper is.
When Kharis is brought back to life as a mummy, he is in a standing position. In the flashback scenes, Kharis is shown to have been buried alive and, without food or water sealed in a wall crypt, he would almost certainly have collapsed before he died and thus should not have been standing when reanimated thousands of years later.
When John Banning (Peter Cushing) relates the story of Ananka to Police Inspector Mulrooney (Eddie Byrne), he states that she died 4000 years ago. However in the earlier scene depicting the burial ceremony of Ananka, it's mentioned that it took place 2000 years ago.
In the scene where the mummy breaks through an upper window and into Stephen Banning's padded cell at the asylum, a large smudge of the swamp mud that covers the mummy suddenly appears on the cloth wall, even before Kharis slides down it, reflecting a prior take.