This sounds like update-specific problems. Have you tried rebooting the OS, and if that doesn't resolve, reinstalling (restoring from the backup you should have taken prior to update - you did take a backup, right?)

Yeah, I know: it's the old Windows support mantra (3R): reboot, reformat, reinstall [1]. But it has clearly helped me before in resolving iOS issues.

[1] http://en.wikipedia.org/wiki/Reboot,_reformat,_reinstall