Low/bad signal on iPhone 4 after upgrading to IOS 6
The only solution that actually worked was a full factory reset:


Make a backup of your iPhone using iTunes.
Using iTunes, perform a full reset of the iPhone.
After the iPhone reboots, disconnect it from iTunes and go through the initial setup.
Connect the iPhone back to iTunes.
When asked by iTunes, choose to restore the backup.
If applications are missing after the restore, perform a full sync to have them re-installed.


I also called Apple support, and they confirmed this is a known and common problem when upgrading to IOS 6, and a full reset is the only way to permanently solve it.