1a) The title bar colour changing feature occasionally bugs out. It will show white over white, or some other non-contrasting colour. This happens with no particular reason as far as I can tell
1b) The title bar sometimes stays on top of a 'fullscreen' app, meaning that for example you have the top title bar icons and text sitting over the camera display view. This happens with no partiuclar reason as far as I can tell.
2a) I have noticed that in the portrait/landscape rotation, sometimes the app veiw gets bugged to sticking one way when the screen display itself rotates. For example, All of the content of the app rotates back around to a portrait orientation but is still trapped in a landscape layout on a portrait display. This is rare but seems to have no particular cause that I can recreate.
2b) The above can sometimes happen in the camera app. When you rotate the camera the icons (flash, hdr, etc) rotate for you. Sometimes rotating it causes them to 'stack up' on one another as if they adjust in one axis but not the other. I most noticably found this when I rotated having had the flash options open (force flash, auto, no flash) and they all collapsed to being on top of one another rather than closing that selection pane.
3) The 'zoom back to home screen' animation sometimes interacts strangely with folders. In that the icons of the folder will do the 'fly out' animation but only confined to the final size of the folder GUI box on the screen. It looks buggy and seems to be a corner case situation. I can't recreate it when I intentionally open a folder > lock my phone > unlock my phone but I've noticed it many times so I should try to pay more attention to its causes.
4) Since iOS9, I can press my 5S's home button to get the screen to light up and recognise my thumb print, but sometimes it will activate siri even if I press it very rapidly. This is a 5S that I purchased in November so I don't believe the home button is faulty. My suspicion is the screen initiation routines on the 5S are a little laggy and sometimes the button registers as a press-and-hold for Siri.
5) Right now I have 2 'unread' emails in one email account, despite there not being any as verified by Outlook on my home PC and the 'unread emails' folder which I added to the mailboxes screen of Mail. I suspect if I remove and re-add the account it'll clean this up but Mail is the only place reporting 2 unread emails.
6) Some apps can have their text input boxes bug out, whereby I can't tap the input cursor part-way back in the window and as I delete text it highlights words and goes wierd. I suspect this may be a buggy implementation in the app itself but I'd have expected that to be a pretty robust UI object, so I figured I'd include it.
Anyway, the above are just examples of the sort of lack of polish I'm noticing build up over time. As said, the biggest increase in it came when they switched to the flat UX design, because I suspect they created so many new UI changes that there were inevitably fresh bugs that had been stamped out in the old design. Nevertheless, a number have stuck around and it's frustrating because I noticed more polish and less of these little rough edges back in the 3GS and even my 4S days on iOS5.
The biggest bugbear is that I don't really know of an easy way to submit these bug reports. I guess I have to jump on the apple dev boards or something but there's no nice way of going 'here's a bug, please consider looking at it or asking me for more information if needed!'.