As I recollect there have been known problems on some systems with Avast 6 gadget and WIN 7.
Have you tried to uninstall the Avast gadget option via add/remove programs, reboot, and see if that solves your problem?
I don't use Avast 6 gadget option, run UAC at default settings, and have never had any issues with Avast 6 and UAC on my WIN 7 x64 installation.