1. Missing notifications. In the beginning none of my apps were getting notifications. After running some of them and uninstalling and reinstalling others, most of my apps are now getting notifications, but there's still a handful that are not.
2. If "Spotlight Suggestions" are enabled in Spotlight Search, then doing a spotlight search causes the "Spotlight Suggestions" to continuously use "Location Services" until the phone is rebooted, even if "Spotlight Suggestions" are subsequently turned off. This is a fairly major bug since it can drain the battery. For now I've left "Spotlight Suggestions" disabled.
3. I'm not sure this is a bug or simply a design flaw, but any app that uses Location Services can run in the background and request GPS location, even if it's set to not run in Background App Refresh. I had a number of apps that were always requesting GPS location after the update since the only options under the "Location Services" were "Always" or "Never". Setting to "Always" means the app can run whenever it feels like updating it's location. Uninstalling and reinstalling some apps caused "Always" to switch to "When Using", which is better. Others seemed to behave themselves better after reinstalling.
4. Settings app crashes, though these seem to have subsided.
5. Phone (5s) gets warn randomly at times for no reason that I can tell. Battery drops during these times. May be related to #3.
6. Can't unselect "Sent" from mailboxes pushed. It looks like it works, but when I go back in, it's selected again.
7. Yahoo Mail via the built in Mail app has been glitchy at times since I installed iOS 8. Mail not pushing, taking a long time to download mail, etc. I don't know if that's an iOS 8 issue or Yahoo issue, but my iPad 2 running iOS 7.1.2 isn't having any problems.
8. Today I had an app update that refused to install. It kept downloading over and over again. I had to delete the app and install manually.