Here are the results of my test of uninstalling & re-installng Avast 6.0.1091

Unplugged Ethernet
Logged off as myself
Logged on as as an Admin user
Switched user to as myself - gadgets OK
Switched user to as an Admin user
Switched User to as myself - gadget positions scrambled
Unscrambled gadgets
Logged off as myself
Logged on as an Admin user
Uninstalled Avast
Rebooted
Logged on as as myself - gadgets OK
Switched User to as an Admin user
Switched User to as myself - gadget positions scrambled
unscrambled gadgets
Logged off as myself
Logged on as as an Admin user & re-installed Avast
Configured Avast
Logged on as as myself - Gadgets OK
Switched to as an Admin user - configured power settings
Logged out of as an Admin user
Logged into as myself - gadget positions scrambled
unscrambled gadgets
Plugged in Ethernet
Updated Virus definitions
(Re)Registered Avast
Sorted out email SSL warning (yawn)
posted here

I feel I have to conclude that this is a Windows 7 issue and nothing to do with Avast - it is also semi-random in that it has occurred at reboot and at switching users by logon/logoff as well as a straight user switch. Just another Windows annoyance to be lived with I guess!