@Morton20
Yeah, can't argue that for sure. I'm still not convinced it is the iOS 5.1 but maybe rather the update process itself. In any case it ***** and Apple really should address it!
Here's a couple other things, you can try.
CAUTION: Always do a backup just prior to doing anything on your device. This will most likely wipe your device and make you set up everything from scratch if you don't have a backup.
You could try downloading thefull 800Mb iOS 5.1 file. Link is from Apple. Place it on the desktop or some folder where you will remember where it is. On the iDevice I would goto reset and select "Erase all Content and Settings". In iTunes, Select your device in the left column by single left click on it. Hold the shift key down if using windows (action key if using Mac) and single left click on the "Restore" button. You will be presented with a file explorer window. Navigate to the desktop or whereever you placed the 800Mb iOS 5.1 file and select it. This will be the equivalent of formatting your hard drive and doing a clean install. You can then "Restore from Backup" which should bring all your settings and apps back.
As a final final resort I would do the above procedure and then just set everything back up from scratch which is a huge PITA.
As a final final final resort, I'd call Apple and explain ALL the things you've tried. If you list them all out, chances are they'll just replace the phone if it's within warranty. That's what they did for me. No questions asked, no troubleshooting steps on the phone. Guy just said, "you've tried everything we would try, I'm just going to send you a new/recertified phone".
Disclaimer: I'm not an Apple Guru, Genius, Tech Support, or Apple employee. Any direction of mine you take is at your own risk. All things I've discussed I've done on my own and family and friends devices but will not be held responsible if you mess up your phone.