When playing through Fez there are many unlocked doors that you need only press "up" on to open. I have noticed as I pass some doors they already appear open, apparently after I have visited that "room". Does the door appear open forever after the first time I enter the room, or is the "appearing open" tied to something else like getting 100% in that room? Once the door appears open, will it continue to stay open forever? I ask mainly because this could be a very useful way of determining where I had already visited (all the doors start to get confusing).
After you open a door for the first time, it will always appear "open" (black).
When you unlock locked doors, the first ↑ will just unlock the door. They'll show as black even before you enter.
It isn't related to progress. Yes, it is somewhat confusing.