Tbh, my game (PC) has run very smoothly. Only one bug, and it only happened twice - my game just shut completely during a loading screen, but both times the loading screen in question would normally have been followed by an autosave, and it did so. Ie, i left Markarth, cue loading screen for Skyrim, and the game just quit. When i restarted the game, i was just outside Markarth, with the autosave in my file. So nothing really even remotely annoying or gamebreaking. So far, the game has run very, very smoothly for me. My only annoyance is the interface and how badly it works with a mouse (i just use WASD, E, R, and Y now, much easier).
I did buy a physical copy from amazon though (which was 5 quid cheaper) which might have something to do with it. Also, the download took 10 minutes. It took 10 minutes for me to install this huge game - i was rather impressed. That plus lack of bugs has made me happy (although the ai can be shitty).
It's a shame everyone else seems to be facing bugs though. I don't think many people got a physical PC copy though?