This a question primarily for TOS fans. We knew of the Mirror Universe through one episode, but no one made as much fuss over it.
How much does/will the alternate universe count for you, compared to the Prime universe we are most use to, especially TOS and its associated movies?
It counts to me exactly as much as, in the context of Star Trek, Anakin Skywalker and Naboo and all that matters.
That is to say, you can argue that it's good entertainment, or bad entertainment. But it's essentially unrelated to the "real" Trek world.
As far as I'm concerned, if they're going to run with the "JJ-verse," I hope that they abandon all pretense of it being related to Star Trek as it's always existed. Avoid confusion about whether Khan was that guy played by Montalban or some other, largely different character. Avoid confusion about how Kirk grew up, or what his solution to the Kobayashi Maru test really was (it's clear that what happened to nu-Kirk is probably not the same as what happened to Shat-Kirk... after all, even if you assume that both are similar, "nu-Kirk" got a serious reprimand while "Shat-Kirk" got a commendation).
These are different characters, on a different ship, in a different situation, in a different universe, and as likely as not, with a different mission.
Treat them as such and it'll all be fine... no need for "jihad" between "Classic Trek" and "New Trek" fans, any more than it's really necessary for BSG fans and B5 fans to have a duel to the death over whose starfighters make more sense.
The problem comes when people start trying to "merge" the two... pretend that something in "nuTrek" is what preceded, led to, or in any way relates to, something from ANY of the prior body of Star Trek work (except, arguably, "Enterprise").
Kirk wouldn't find the Botany Bay in this new reality, because the odds of him just HAPPENING to be in the same place at the same time, given all the other differences, is beyond astronomical. (Maybe, in this altered timeline, Clark Terrell finds the Botany bay, many years later on?)
You can toss out any "continuity" whatsoever which predates the "Nero pops back" incident. Whatever this is, it's not, and shouldn't be treated as, anything "of a piece" with any prior Star Trek. It's not. Everyone will be happier if they stop pretending that it "is, sort of."
I didn't think that this movie sucked, though I don't think it was fantastic, either. I just think it wasn't Star Trek, and wish it hadn't pretended to be.