You could also have it where if you get a certain number of best answer votes in a category, you get the "Expert" badge for that category. That would be easier than and fairer IMO than having the mods say who gets the badges.
This is by-far the best idea I've read.
Logic: If # of best answers exceeds (given number) in board X, automatically update user's member-group to board X expert.
While this is a brilliant idea, it's problematic because the forum isn't designed to work this way. I would have to create >20 new badges, each one saying expert and the name of the board (which won't fit in the image, see below)...

This would also require a considerable amount of coding, though it can be done. That's the beauty of coding, everything is possible. What would be easier is this logic:
Modified logic: If # of best answers exceeds (given number)
in board X, automatically update user's member-group to
board X expert.
This is something I can do
quite easily. I could also create a few new badges... Recall that badges and member-groups are two different things. For example, someone is awarded the science/math/physics/etc. expert badge. This would have to be a manual edition though.