Just updating this issue. Yesterday I completed the final arc I had left in the 35-39 range. When I went back to see if it had completed, I noticed that all the missions in the 35-39 range were now complete (including the previous ''They Call Me the Doctor'' mission).
So I believe that completing all the missions within a level range will fix this issue. Can anyone else confirm?
Found another mission, “Manticores Wedding Woes”, which is also not getting a star once compleTed.
Like Molubdos, I have the Doctors ally badge, but no star for the arc. Manticores wedding gives no badge and still doesn’t complete.
I received an email from a GM Miss asking about this issue. I can never reply to those emails, keep getting error messages, so I'm hoping she sees this, as it contained the answer she was looking for.