I've been having very similar problems with my game. Since early access I'd log in and find PCs and NPCs would take minutes to load in, and running or walking through Limsa would make me fall through or get stuck in the floor. Also happened on a chocobo porter in Thanalan once and I fell through a bridge. I thought it was a lag issue until I saw this topic.

Fully updating Windows and updating my nvidia drivers to beta seemed to fix it, but half the time I start the game up now it takes an incredibly long time to load in characters, audio breaks and menus take a minute to appear after clicking on them. If I logged out sitting down when I log back in it's just stuck on a close up view of the stool or floor I'm sitting on. When it's broken like this it sometimes crashes. If I exit and restart the game a couple of times it's back to working perfectly.

Since I don't crash a lot I'm not sure if this is a separate issue, but the symptoms are the same anyways. I use Windows 7 64-bit.