When the Mummy is first awakened and travels to the Banning house, one of the neighbors is awakened by a shadow moving across her face. She wakes up her husband to tell him. He then looks out the wrong window to try spot the cause of the shadow. The moonlight comes in from a different set of windows.
George Zucco confirms that while it didn't kill him (being set afire at the end of The Mummy's Hand), it "maimed and distorted" the mummy, which neatly explains why Lon Chaney looks nothing like Tom Tyler, it does not explain why the wrappings on Chaney's mummy are not even singed.