Should I have “Scan Secured Connections Checked”? And what does this actually do?
This checkbox enables scanning of HTTPS (webshield) and IMAPS & POP3S (mailshield) traffic. It significantly increases your network security, so it is a good idea to turn it on. On the other side, it is a quiet new (currently available in the beta only) and non-trivial feature and may have some side effects (especially on HTTPS). The default state is ON for the mailshield and OFF for the webshield.
More info on SSL scanning can be found here: http://public.avast.com/~tuma/techinfo/