1: Apps don't download from the App Store the first time. I need to try 3 or 4 times.
2: Swiping a notification from the lock screen frequently crashes springboard.
3: In fact, switching apps frequently crashes springboard.
4: Music didn't download from iCloud properly.
My friends have different bugs, as well as my iPad, which is interesting. One friend didn't have his reminders work for a while.
As an aside - Xcode 5.0.2 is extremely buggy too. But we know Apple loves it's devs.
I forget exactly which, but I think I've seen it in Apple apps too. Mail maybe?
I've found that entering and leaving Airplane mode fixes things, presumably because it causes the phone to notice which cell it's actually connected to now.
In order for this to be effective in the app you have open, though, you have to stay in Airplane mode long enough to time out whatever TCP connections the app is attempting. Tower-switching is a purely physical/routing-layer effect, so you still have the same IP, and TCP connections stay established. If you trigger the carrier renegotiation without staying in Airplane mode for long enough to drop your DHCP lease (usually about three seconds, I think?), the phone will go on waiting for a reply to a TCP SYN that never actually hit the tower, so you'll find, like you said, that you may have to kill-and-restart the running app to get it to work.
Dropping internet connection does occur on WiFi and is not fixed in the iOS 7.1 update.
When I come back and hit play, most times it'll play out the buffer and then decide it has no internet connection, fixable only with a kill-relaunch. And some times it'll reboot the device altogether.
I also had an issue where around half of my music got corrupted during a sync. It acted like everything was fine, then as soon as I tried to play a broken song it would just skip it. Which was particularly irritating because it made "previous song" via 3-clicks on the inline play/pause button stop working. I'd have dead spots in the middle of playlists that I couldn't rewind past because it would hit them and immediately jump to the next song.
Resyncing seemed to fix the audio, but ran out of space because it left behind 4 gigs of cruft in "Other" that the storage page in settings couldn't account for anywhere. I had to do a restore to get everything working again.
So all in all, my experience with iOS 7 haven't been great.
EDIT: One more complaint in the design department, even though I don't mind the iOS 7 style as a whole. The new Music app is very clearly designed for the iPhone 5 and up with taller screens. The scrubber has gotten a lot harder to use, and if you're not precise enough you'll end up setting the song's rating instead.
I don't think I've ever had an acceptably performant session in the App Store, at any time of day, on any device, from any network. Even direct links to app pages from other web pages have always been slow.
So I'm not one who'd be able to notice new 'lag'. But I haven't had any crashes.
The "Other" space tends to be MMS messages. If you're not manually clearing conversations, those pictures, videos and sound files are just getting filed away forever. They really need a fix for that. If nothing else, offering a setting to automatically trim conversations to only the most recent X weeks.
The Other space ballooning definitely coincided with the music syncing bug. Before that it was a barely noticeable sliver in the space meter.
As far as App Store, that one actually runs well for me. It's only the music store that sucks.
* the music player corrupts itself and starts skipping all songs, may or may not be fixed by rebooting the device. May require resynchronising all the music (remove/readd everything)
* it regularly decides to stop opening sync sessions with iTunes and has to be rebooted
Apart from that it's been pretty smooth sailing.
Oh yeah, and every single update re-enables bluetooth, that's annoying.
Then again, I wouldn't say I'm a heavy user. I mainly use it to check on my mail, read some news, etc.
Was it really a restart or just the UI (springboard) restarting?
The cell phone modem is a separate hardware piece in your phone, it has its own operating system. The smartphone OS communicates with the modem over an interface usually using "AT" commands. The iPhone 1-4 had an cell phone modem design by Intel (GSM version, modem manufacturer got bought by Intel).
The iOS UI consists app(s), so it may crash and restart.
Otherwise, I haven't had any issues.
Really hoping this was fixed in 7.1, which I'm running now and so far seems smoother (doesn't stutter anymore when switching to the task switcher view, for example).
The other persistently anooying bug I've seen has to do with text fields on some webpages (eg Outlook Web Access and the Amazon Kindle web app) where if you tap to change the cursor position inside the field, you can no longer type characters in it and have to deselect the field (by tapping another on the same page) and then reselecting it again. Makes fields on many pages simply un-editable (the Amazon web app is the worst as you have to leave the store section entirely and it breakd the product Search field). Not sure if it's page or Webkit specific but it'a been around unfixed even on iOS 6 if I remember right. Fingers crossed on that one :)
b) I have itunes rental downloads stuck in a quasi state where I can neither finish the download nor can I delete the download.