I can't think of any specific Star Trek related items that would ruin it for me. There is nothing I "need to see" or "hope I don't see" from a Star Trek standpoint except that I hope the familiar characters act "in character".
Being that this is simply a movie, I want it to have the qualities of a good movie (interesting and consistent characters, thoughtful and [relatively] believable plot, fun to watch). If those qualities are missing, then that will ruin it for me.
Let's see, how about an aimless drunken Kirk. I'm surprised he didn't burp before he said 'Jim Kirk.' And that is a high five from my POV.
Well, yeah -- but if there is no reason given in a film for a character's out-of-character actions, then that falls under my general wish for "consistent characters".
Acting in a meaninglessly uncharacteristic manner is not a potential problem that would be exclusive to Star Trek, but could happen in any film. The one small difference here is that the TOS characters' traits are pre-established.
The "aimless, drunken Kirk" is OK... provided that this is the "alternate reality Kirk" and things get fixed during the course of the movie (so that the guy we see at the end, albeit played by Pine, is "really" the Kirk we remember).
This is actually somewhat borne out by what we've seen so far. We see Pike as the captain, but we also see a shot with Kirk wearing what we believe are captain's stripes. So, either (1) Kirk "goes from academy to command overnight" or "the timeline gets reset and Kirk is back where he was supposed to be at the end." (albeit on the new sets... )
Playing the "what if Kirk had grown up in a different situation, in a different reality?" may be a somewhat unsatisfying story for a film (much more fun in a series, of course... we've seen plenty of those "mirror, mirror" type stories and it's always fun to see alternative takes on characters we know!), but it could turn out well enough.
If we're seeing "hints of who he's supposed to be in the correct timeline" showing up, leading to him being responsible for putting things right, perhaps.
If what I'm seeing re: this film is correct... from the prequel comic and other sources... what if Kirk saves the day (after Romulus is destroyed, after Nero travels back in time, after Kirk's dad is killed, after Kirk is left a drifter, after Kirk screws up at the academy but still gets on the Enteprise, after Pike is taken out, Vulcan is destroyed, etc.) by doing something that, ultimately, saves Romulus? By saving the Romulans, he prevents it all from happening... and everything gets put back how it should be, in other words.
Wouldn't that be something?
And all we'd have to "retroactively fix" would be those final shots on the Enterprise bridge, and potentially the exterior of the ship... but JUST in those shots.