Since you have spoken to the staff on that floor about the situation, I would take it one step further...speak to the administrator and advise him/her that if the problem is not rectified today, that you will consider notifying the police of his behavior and that if push comes to shove, you may need to file paperwork on this man.
He should not be roaming around the halls and going into other rooms. If they are aware that he has issues, then they need to move him closer to the front desk where the staff can monitor his movements and yes, a bed alarm needs to be placed on him and the bed.
If he has memory issues, then he needs to be moved to the memory unit. I'm sure your mother was scared to death w/this strange man in her room. Unacceptable!
Sit quietly, the answers will reveal themselves when you least expect them to. The past is gone, the present is a gift and you need to focus on today, allow the future to reveal itself when it is ready.