Same problems here. Country: Italy, carrier: TIM.
List of problems spotted so far:
1) Internet connection randomly lost: even if the status bar shows full bars 3G coverage, it will not be possible to load any web page (or use data whatsoever). The only way to get it back connecting to the internet is turning airplane mode on & off, or rebooting the phone.
2) data connection completely lost during calls. While on a phone call, the status bar indicator switches from 3G or E to blank after 1 or 2 minutes, and it is not possible to connect to the internet. When I hang up, the data connection is restored and the status bar indicator returns to E or 3G.
3) I get edge (E) connection where I should have 3G. It's like it doesn't switch from E to 3G when it should: when I get home I park my car in a garage, where there's little coverage, so the phone switches from 3G to E. Then I walk home, where my wife's iPhone 4 has 3G connection (same carrier I'm on), but mine remains stuck on edge. The only way I can get it to switch to 3G is, again, turn airplane mode on and off, or reboot the phone. My former iPhone 4 would always switch back to 3G as soon as available. Same garage, same home, same carrier, same SIM card, same iOS version (5.0 and 5.0.1).
Problem 1 is the most irritating as it happens randomly and without notice: I have connection, I put the phone back in my pocket, take it out one minute later and I can't connect.
Problem 2 is not a big deal (for me), but it clearly shows something is messed up *badly* in how the phone manages data connections.
Problem 3 is a pain because every time you get E you'll be wondering if there's actually no 3G coverage or if it's just the phone being stuck again.
Two last remarks:
a) my previous iPhone 4, 3GS and 3G worked smoothly on the same carrier with the same SIM card I'm using on this one (I've had it cut down when I switched to 4).
b) I've tried everything possible to fix it: I have no PIN lock, I've restored network settings, I've even completely restored the phone and set it up as a new phone, I've tried with manual carrier selection, I've tried changing APN, all sort of things, but nothing worked.
I'm thinking about having it swapped, but first I'd like to understand if it's a software issue or a hardware one.