Garr, this is really annoying in Leopard. Too bad there isn't a global admin setting to set this to STFU!!!
Anyways, after some research, found that items downloaded into the Downloads directory get flagged with com.apple.quarantine. Everytime you start the app, it has the Vista'ish question, "Cancel or Allow?". Isn't this the basis of a Mac Ad that made fun of Vista?
Any hoo, this feature is very annoying. What else is annoying is that the orgination Admin user has to OK it. Not another user with Admin priveledges, that would make too much sense! Oh noes!
I found a better way by just parsing all the apps in /Applications ( xattr -l *app ) and doing a quick com.apple.quarantine scan on all the downloaded apps for the students. Then just apply 'xattr -d com.apple.quarantine naggy*.app'.
I hope in Snow Leopard, they shit this frakken thing off, or make it a "Please STFU" Preference Pane.