Since the iOS 6 update I have had the same issues on all of my iPhones. After the update my devices connected without any problems except internet hotspot didn't work anymore to my tablet. I reset the Networks and this is where things got out of hand. Suddenly I couldn't connect to my wifi networks anymore (same ones I was connected to) but internet hotspot was working... I did everything people suggested... updating firmware, resetting network settings, changing channels and in the end it was a SIMPLE and stupid fix...
Now here is the most simple solution - Just pointing out what a bad job Apple did with this update to iOS6!
When entering the password for the wifi router I press the "Join" button where I get the message "Failed - cannot connect to wifi"... Now - Just press Join again... voila! Without changing the password or anything - suddenly it connects!
I would be interested to know if this works for other people too?