It would be nice to allow a user group to edit their own blog posts but not give them the full moderation capabilities.

It’s a setting in the group settings:

 

7 hours ago, opentype said:

It’s a setting in the group settings:

 

Yes, but note the behavior:

The user will be able to: edit comments and entries, delete comments and entries, and lock entries from further comments.

Basically they become a moderator of that Blog. What @Josiah Wallingford is requesting (and what should be available by default) is just an Edit Entries permission.

I disabled the permission above and I can edit my entry (as a member):

Make sure you have Blog Entries enabled in the Groups -> your group -> CONTENT tab -> Editing:

Check the time too.