I've managed to also find that Institute bug on Day 1. I think it is related to the Maid job and if you get the old man scene. If I do the maid job and don't get the old man, I can proceed into the Institute without an issue, but with the old man scene it crashes when entering the building.
Save 2 I didn't get the old man scene, and doesn't crash.
Save 3 had the old man scene and crashes.
Is the only difference between the two that you got different results at the inn? The second save does indeed have the problem, but I can't get the issue to repeat in my own save when I meet the old man. Can you remember anything you did different between the two saves?
Edit: I think the bug happens before, and getting the other result at the inn actually "fixes" the bug, while the old man encounter leaves it as is.
Second edit: I think I found a solution, although the actual source of the bug eludes me. For some inane, baffling reason, the first variable of the game isn't set to 0 at the start of the game (that's the default value). All I did was set it to 0 manually right after the start of the game, and everything works fine. What's even more bizarre, is that after I "fixed" it, the variable works as intended even If I delete the fix.
I assume there is an issue with one of the scripts, and I might have to investigate them one by one to see if I can figure it out.
Long story short: the bug happened as soon as you fired up a new game (but it was often "masked" when the variable was used, and this specific variable is used all over the place, hence the seemingly "random" nature of the bug), and it happens before any of the in-game logic is used (which is why I couldn't find it looking through the events of the game). Its behaviour is really weird, which is also why it was hard to find. At least the fix is easier than figuring out why it's happening. XD
Thanks a lot to everyone who helped with this.