Box of Tricks

In my experience, for both fanfic and original fic, the main beta focus areas need to be consistency (of voice, as well as things like the car colour...), plot holes, awkward scenes, the need for explanations, Americanisms, anachronisms and, of course, grammar. Canon can be sorted via things like the Hatstand site and besides, if you don't have a really good grasp of episode detail you will be writing your own episode rather than trying to 'fill in gaps'. I think betas who aren't familiar with canon are fine because your story should be accessible to readers who also aren't experts. They can pick up on where you should add more explanation, something a fandom expert might miss. So - ask your f'list and then find a first reader who has some canon expertise just to make sure...