What!? You came to NH and didn't drop by to visit me!?
I have a growing list of haunted places in NH. I don't recall seeing the Mt. Washington Hotel on the online lists I've read, but it wouldn't surprise me if it's haunted given its age and history.
Given your finicky lock situation, who knows. It could be a finicky lock... or a prankster ghost!
We'll have to pay the place a visit next time we're up north... I wonder if I'd feel anything.