When you create a forum for just one group (group-awareness), all the people in this group (with contributor role) have no problem to create a thread, reply a thread and even edit own reply. However, the owner cannot delete his own reply message even though that he has the delete-Own permission (10% time it works, I need to say). This is only happening for a group-aware forum. On a normal forum, it works fine.
The error message is:
Alert: You do not have permission to delete this message.
For the test plan, you can try to reproduce the steps mentioned by Earle, but it sounds like it's random/hard to do. Just make sure that group forums/topic are working as expected.