Thanks for playing and for the bug reports!
I updated the demo with a few changes, including the removal of locked doors (I also experienced that bug a couple of times but couldn't recreate it at will and couldn't understand the cause so for now this is my best option), locking the mouse cursor (partly to get rid of that UI glitch, partly because you don't really need it), and adding a couple of graphics options including V-sync. I couldn't really notice a difference while testing, but maybe you will (or maybe I didn't implement it right lol).
If you feel like giving this new version a try, that'd be great.