Here's one for a new user: Let's say I'm looking at apps on my home screen, swipe left or right to see more apps. Great. I install something new. Not on the home screen. Swipe left or right. Not there either. This is an actual problem for normal users.
I also don't like having to pull out the battery every few weeks because the phone is frozen when I picked it up off the dock. This can happen from any background app. In the most recent case, turns out it was the foreground app, a clock called "Alarm" that I had coming up when docked in the landscape dock. Switched to Daydream, that problem went away, at least. But having to unplug the battery before I can make a call, definitely an annoyance. Glad it has a removable battery though, disassembling and reassembling the battery saves me having to press Home + Power for 10 seconds.
Ha, here's another one, as I'm writing this.
I just took a picture to talk about the UX of finding and sending that picture, but when I went into Apps and swiped left to look for Gallery (seriously, we can't just call it Photos?), the phone froze. Now I'm looking at the first page of icons half off the left of the screen, above a dimmed set of the second page icons. It's still stuck there as I type this. But the phone isn't frozen, I was able to take a screenshot of the built-in Apps browser being stuck halfway between two pages:
https://www.dropbox.com/s/z04qqbn4a93sxlb/Screenshot_2013-03...
As I'm finishing this paragraph, it's still stuck. By contrast, I haven't seen an iOS device crash swiping between the app icon pages.
While finishing describing the above, the phone dimmed, and then locked, as it should. I unlocked using face recognition, and was looking at home screen. Tapped to browse apps, and ... still frozen halfway between two apps pages.
This is native core functionality, simply not working. And like now, these things happen when trying to do something useful. That's a user experience annoyance.