Okay, I think I managed to fix it.
Make sure you are not using any mods (smithing ones seem to cause bugs in this update)
1. Delete the Skyrim - Interface.bsa file in the Data folder.
2. Go to Steam, right click Skyrim, then go to Properties>Local Files>Verify Integrity of Game Cache.
3. It will verify for a bit and then say that there are 2 or 3 files missing, and that they will be replaced.
After that, the mouse1 problem was totally fixed for me, though you will have to redo your settings (like subtitles and unticking the xbox controller box)
Arrow keys do not work, but I'm pretty sure that's just the patch being fail.