Skyrim runs fairly well on my machine (Linux Mint 12 & Crossover 10.3), but it does have a couple of issues:
1) When first launching the game you get the Bethseda logo; and then sometimes nothing else. Most of the time it launches just fine however. It's strange and random which defines most of the bugs I've found. One thing that does seem to help keep it from going to a black screen? Hit buttons on the keyboard randomly. As I said... strange and random.
2) I had quite a few mouse issues when first starting. It was often buggy, laggy, and often skipped randomly, but digging around in the Wine DB as well as editing the skyrim.ini file for about an hour checking settings I finally got the mouse working well on my machine. I couldn't even begin to remember everything I did; although I do believe it's most system based anyway.
3) Fairly rarely when walking/running you will just keep moving even after you've let the key go. This is often seen during combat when your hitting keys very quickly. Generally just smashing the movement keys (WASD and spacebar) randomly for a second or two stops it.
4) If your running in windowed mode unchecking "allow the window manager to manage windows" in the winecfg while fix some mouse and camera issues, but it does cause a few problems itself. It is worth a try however.
One thing to note is that the camera itself lacks fluidity. It is not a bug or a problem; it just normally feels strange, but you get use to it after a while.