The problem: Messages that blink into the inbox and "disappear"
Wasted user time by Notify and Mobile alerts of new messages that are actually Junk or other rules processed that quickly are gone from the inbox, but the user was still put on alert. One example is support staff getting waken up to alert mail that turns out to not be urgent and the rules otherwise handle the message. While it is rare, it can be VERY disruptive.

How: That there be a speed bump of some sort in the POA to handling new messages to make sure rules have a change to run before a message actually appears to the user client or SOAP (GMS and WebAccess appearance). I think there should be a time limit on this (something under 5 seconds), with errors showing in the POA when that time limit is exceeded to help identify excessive rule sets or other resource constraints.
Process flow would be for new message to arrive but be unavailable to Notify or SOAP until the rules have processed or X seconds, which ever is first.