I would suggest this is one of 3 things:
a bug in CM6. I used Handcent regularly in CM7 and didn't see this behaviour.
Possibly related to having Handcent / some other MMS app installed. All apps have registered to be told when a message arrived, and all apps are capturing it and inserting it into the telephony MMS/SMS database. This seems unlikely, because apps will normally rely on the built-in app to insert the message into the database.
This could be an issue with the interaction with the network, and acking of the message, which is causing it to be notified multiple times.
I think the best thing to do in this case is capture some logs using ADB and logcat, and posting them on the Cyanogen forums where we can take a look at them and figure out if this is a bug. If you aren't comfortable using the development kit there is an app on the market called aLogCat, which will grab the log for you, and allow you to send it to an email address.