For SeaMonkey (v2.19), zilch, no activity.
Opera (v12.14) scripts also don’t make it into the Scripts report. No activity, other than it started.
I even turned on reporting for everything including OK items just to see if the problem reported here about Firefox also includes SeaMonkey. It appears to be so.
The per-site NoScript in SeaMonkey here permits some scripts, denies others. Still I’d think Avast would see them all first.
For this site and few others in Opera I also allow scripts to run. So I’d think Avast should see them.
Or tell us to not even bother installing ScriptShield to save precious resources.
Now, it does appear that something is being checked by the WebShield, for instance these log entries are from this forum
http://forum.avast.com/index.php?board=2.0 [+] is OK
http://sf0.iavs.net/Themes/default/scripts/topic.js [+] is OK
http://static.avast.com/shared/j/s_code.js [+] is OK