Correct me if I'm wrong, but Avast seems to proxy Web and Email traffic (assuming that's enabled)
One of the things that I notices is opscd becoming quite taxed after installation of Avast. Using Outlook/SSL to company Exchange server, along with general web browsing was sluggish and the application process would become unresponsive.
Disabling Avast would seem to make the problem go away, so immediately blame that.
However, after a bit of inspection I found two other shims in my case that caused issues.
1] opscd, the CRL database in /private/var/db/crls had some entries with dead TTL that Avast simply didn't seem to know what to do with. Therefore opscd would see the TTL expired and would try to interogate a CA, which Avast would intercept and simply cause a race condition (because the TTL was dead, invalid, bad hash, etc)
If you're slow, trying making a backup of /private/var/db/crls, and then remove ALL of the entries (not just the .db entries)
(sudo rm -rf /private/var/db/crls/* && sudo rm -rf /private/var/db/crls/.fl*)
2] Cisco Anyconnect, or Legacy Cisco VPN client. In OSX 10.6 or better, where users upgraded from Leopard to Lion. Artifacts from previous 32 bit apps may hang around. One of which is the VPNd process shim from Cisco. Assuming you have/had this installed, I would suggest you uninstall by running the Cisco uninstall script. (sudo /opt/cisco/vpn/bin/vpn_uninstall.sh)
As always, make a backup before you make these changes/execute at your own risk/etc.
If you're web related performance issues with Avast, hope this helps point some people in the right direction.