Even assuming the magic is possible--that a village in the Scottish highlands could vanish in the 1700s and reappear for one day every hundred years, its inhabitants looking more and more anachronistic with each reappearance--the timeline still makes no sense.
If it were the 1700s when this miracle got instigated, and it's the 1900s when our two American heroes stumble upon Brigadoon in its one appearance during the twentieth century, then gosh, let's do some quick math: In Brigadoon time, the miracle began two days ago. They're placidly walking around as if totally used to it, when anyone who truly lived in such a place would still be going, "Holy *^&@! It's seriously another hundred years later out there?"
Couldn't they have made it reappear, say, every twenty years? Then at least it would have been going on for ten days in Brigadoon time; and twenty years for the outside world is still enough time to be a romantic obstacle.
For that matter, if it's such a remote village, and the citizens are not allowed to leave it, how do they even know the miracle's working? If, in Brigadoon time, no one from the outside showed up yesterday (i.e., the one appearance in the 19th century), how would they have any idea whether a hundred years had really passed or not?
Also, the linguist in me can't help pointing out in this and in all other time travel stories, there's no way the inhabitants of an 18th-century Highland village would be easily understood by 20th-century Americans, or vice-versa. The dialogue really ought to be all:
FIONA: I'se gang wi' thee, lad.*
TOMMY: Sorry, what?
In short, if I'd come up with the idea of Brigadoon, I would never have written it, because all the practical difficulties would have doused my inspirational spark within five minutes. Surely the difficulties occurred to the actual writers too. So how did it get written?
My conclusion: the story is romantic, and the music is great, so everybody dismisses all the outrageously bad plot devices and enjoys the show. It's totally unfair, the passes that musicals get as long as the songs are good.
On the other hand, maybe it means I shouldn't stress so much about believability in my stories, especially the ones with paranormal elements. Readers or viewers want their disbelief suspended. They only ask that you help hold it out of the way with your delightful storytelling, no matter how ridiculous.
Good to know.
Waitin' for my dearie (to get home from work),
*Stolen shamelessly from a Robert Burns poem.