Played for about 12 hours and here are some bugs I (and a friend of mine) have encountered:

• For some reason my friend's laptop has issues with the mouse - while in the menus the game does not detect the position of the cursor, making clicking anything impossible (he is forced to use the keyboard just to leave the game, and cannot rotate items in the inventory as a result).
  
• Sometimes quickly selecting the same spell for both hands very quickly via a hotkey makes the right hand disappear (the whole frickin' arm, not just the spell) in first-person. Dual-casting works however - you just don't see the second hand in action ).
  
• Clicking an item category at a vendor with the mouse and then clicking another one (some time) after that causes the bartering window to close (dialogue continues as if you closed it yourself). Doesn't happen when done with the A and D keys.
  
• The bigger Frostbite Spiders in Helgen's Keep fail to descend to the ground and are stuck mid-way for a brief time. During that time they were sitting ducks for my attacks
  
• When I went to Riverwood with that Stormcloak I escaped with (can't remember his name, for the life of me) and later talked to him at his sister's house at the table, he was sipping some brew from an invisible mug during our conversation.

Requests for the UI in future patches:

• Add a way to favourite "Unequip anything that's currently in my left hand". Currently, the only good way to go One-Handed Weapon only (for blocking) is to go to the favorite menu and equip another One-Hander to the left hand, then instantly unequip it before leaving the favorites window. So you kinda need to drag around another weapon just to switch between spell+sword and sword-only. Makes no sense at all
  
• Navigating the perk constellations is uncomfortable: using the directional keys doesn't always follow the lines to the adjacent stars (instead skipping over to higher/more distant perks) and the other perks aren't always on-screen to click on. I'd suggest reducing the scale of the distances between perk stars so that more of them are on-screen at a time.
  
• When buying spell-tomes from a vendor, please gray out the spells already learned.
  
• Please split the Misc. category in the inventory into Misc. and Smithing to have a clear category for all smithing ingredients. Because right now it is difficult to find the truly "miscallenous" items like, say, a Golden Dragon Claw .