I file under Who Cares. As far as I'm concerned Scotty could sport a "full kit" beard in the new film. He could have shaved prior to Where No Man Has Gone Before, so it's not really an issue. I know some of the spin-off media (novels and comics) suggested Scotty grew the moustache he wore in TMP at some point near the end of the first mission (IIRC that's also when he started to go grey according to the spin-offs ... though for all we know he could have been using Grecian Formula 2362 since the days of Chris Pike), but this is one of those issues that doesn't really make a lick of difference to the canon. Heck, the movie could take place between episodes of TOS and it still wouldn't matter as long as you have a razor. Most men can grow a pretty full moustache in a week.
Cheers!
Alex