I've been noticing a few random issues with my iPhone. It's hard to say whether they're related to the new iPhone 5 or iOS 6 since I made both of those updates back-to-back. Specifically, my iPhone was no longer showing up in iTunes to sync over Wi-Fi and I was having some difficulty with Tweetbot's iCloud sync feature. Who knows whether these things were related, but one thing they did have in common were requiring network connectivity.
I tried other troubleshooting methods like reinstalling apps, resetting the iPhone, resetting the wireless network and nothing seemed to help. Some of my twitter followers suggested Resetting my iPhone completely, but that seemed a little drastic and would require a full restore of the device. As an alternative, I instead choose to reset my iPhone's network settings. This can be done by navigating to Settings > General > Reset > Reset Network Settings.
After the reset your phone will reboot and you'll lose all your preferred Wi-Fi networks and passwords so you'll have to re-join them manually. But since the network reset, Tweetbot iCloud sync is working again and iTunes can see and sync wirelessly to my iPhone. The latter is a huge deal given my current shortage of USB to lightning cables (I keep one by my bedside for charging and another at the office.)
Unfortunately, like many others, I'm still noticing some Wi-Fi fluctuations that weren't present with my prior iPhone and iOS 5, but my problems have never been serious enough to cause interruption in service so it's not a big deal for now.
If you're noticing networking issues on your iOS devices, don't forget this troubleshooting tip.