I completed the Referee clinic but my member record only shows a Referee Certification. There is no certification as a Scorer. Do I need my record updated to reflect that?

No.  The online Referee clinics have both Referee and Scorer modules in it.  A referee has to complete all modules of the Referee and Scorer clinics in order to get certified.  So, a Referee is automatically certified as a Scorer by default when they complete the course.  The online clinic will only allow us to associate one certification to the course so we are updating the Referee certification only.  It still means a certified Referee can work as a referee or scorer during the events. 

If you take the Scorer ONLY clinics, then the Scorer certification will update in your member record.  If that is the only certification you have in your record, then you can only participate as a Scorer at tournaments.