I've had a few minor bugs, but only one major one. I was attacked by a purple dragon outside solitude and the game crashed as I delivered the killing blow. Fortunately, I had quicksaved about halfway through the fight and when I loaded up the game again, the dragon was the normal colour and the game didn't crash when I killed it. So far, this has been my only crash.
Let's see...
The house of Aventus Aretino has several sections of the wall and floor missing. Restarting the game doesn't fix it.
Sometimes after crouching my character doesn't stand up properly. The sneaking crosshairs disappear but my character remains crouched down. Pressing the key again fixes it.
In the town of dragon bridge (I think) there was an old woman sweeping her front porch wearing nothing but her underwear. I don't remember her name, but she gives you a quest where you have to retrieve her husband's secret stash of alcohol from a cave. I actually don't know if this is a bug or not... It could just be something she does.
Finally, the underwater sound effects are weird for me. And maybe it's because I'm an argonian, but every few seconds while swimming my character will make that gasping sound, even when I haven't surfaced.
But yeah, other than that the game has been running well. I'm on the PC, by the way.
EDIT: I also lost Lydia for several days. She eventually caught up to me, though.