As Eddie leaves Dr. Nolmar's building with her he gets out the elevator and turns to the front door, seeing the men hunting him he turns back. In this short period of time the elevator has delivered her to the basement and returned. The door opens immediately he presses the call button.
When Eddie gets attacked in his apartment you can briefly see sound stage floor dust on the soles of his feet. He had risen from bed when the attacker broke in and wouldn't have had such dirty feet.
When Eddie walks though the metal detector in the hotel near the end of the movie, he gets through with no issues, despite the fact that he is clearly wearing a metal belt buckle.
It makes no sense for the electricity to still be flowing, or for hi-tech equipment to still be functional, at a facility abandoned years before.