NOT a big deal. But it probably ought to be fixed eventually:
If a member who is new-member-moderated sends a message, and a moderator claims the message and edits the message and then approves it, the fact that it was edited doesn't go into the activity log.
If a member who is new-member-moderated sends a message, and a moderator claims the message and edits the message and then approves it, the fact that it was edited doesn't go into the activity log.
Given that you have to go into edit mode (whether you make a change or not) in order to claim a message, I think having a separate Claim option for a message (which has been suggested several times before) would be good and mean that any Edit action logged is more likely to occur when an actual edit takes place.