There are a couple of bugs I've found so far that weren't there in 8.0 with the January patch
1) Memory management seems to be an issue because my music player seems to randomly stop when the music is playing with the screen off. I've checked other apps & it's the same issue.
2) Headset button function seems to be messed up again. Initially it wasn't working correctly, where a skip command would carry out a double skip, then got fixed in the December patch & now the issues is back again. The app developer has confirmed this is an OS issue.
3) Notifications on a secured lock screen are all collapsed & cannot be expanded. When the phone is unlocked they display properly, expanded, in the notification drawer. This doesn't seem to be a 8.1 specific change that Google has made so there's something wrong. Again this was how it worked in 8.0 & I've checked the notification settings for the application & they haven't changed since the update.
This is what I could find for now but I'll add on if there's anything else. The Memory management bug is really a show stopper.