I was able to successfully modify permissions for 2 moderators on your site, and changes were still there on second view. Even though both should pull the same permissions row anyway, this could be an issue with moderators that have 2 moderator rows for a given node. I think this is only possible for imports of super moderators, or if you explicitly create the same moderator twice without realizing it. I added a check in the DM for the next release to make it impossible to add the same moderator to the same area twice.
You'll need to remove the duplicate moderator entries (e.g. if a moderator has 'All areas' twice). Once there is only one row for each moderator, they might start pulling the permissions you expect.
As for the group "moderator permissions" being "Not Set", I found a bug in the importer while going through your logs that caused the values to be lost for this group during an import. However, this would not prevent you from being able to change them in the future.