I guess our brains were off, then. For what it's worth, MoviePlotHoles identified only two major plot holes: that the Enterprise basically deserted Kirk on an ice planet, and that stars don't just suddenly explode. If you think either of these is sillier than anything seen in Ye Olde Trekke, I can't help you. (For crying out loud, the Enterprise travels back in time - and then forward again! - in Star Trek IV by slingshotting itself around the sun.)
OK, you asked for it.
First off, the grandfather paradox. The Romulans go back in time, and radically alter the time line. Right off the bat, there's a problem. Even if they don't kill the people they believe to be key players in their situation, they alter the people by causing a cascading wave of other situations which either won't occur or will occur in such a radically different way that the other people won't be the same people--their fundamental experiences of life will be totally different. MAJOR PLOT HOLE.
Romulus is destroyed by an explosion at the center of the Galaxy. <blink></blink>(blink)At. The. Center. of the. GALAXY???? (blink) Think about that for a bit.
Future Spock comes back to do what? By the time he leaves, it would be a differnt future Spock. Or are they giving him the BttF timelag window to try to fix things? Which becomes impossible once the planet Vulcan is destroyed.
If that a drop of that red goo can create a black hole, why do they have so much of it on the spinney ship?
The Romulans show up, blow up the fleet, and then... wait 20 years. What are they doing for those 20-odd years?
"Enlist in Starfleet." Um, that would be "Join and be a jr crewman". "Enroll in the Starfleet Academy" would have been what Kirk needed to do to become an officer, and get his own ship within 5 years.
The car scene--totally pointless. Actually, I have heard a back-story explaining that scene, which was pretty neat, but since it isn't in the movie, it has to be at best EU. As such, the only reason for including it in the movie is that it was in the trailer. It does nothing to advance the plot.
Why do the academy crews take off in shuttles? Aren't the transporters working? Transporters can move 6-12 people at a time every minute or so, and there are 4 transporter rooms aboard the TOS enterprise. Seems to me they could really speed up that boarding process.
There is a really funny editing glitch in the fight onboard the romulan ship. Kirk jumps. Misses. Lands next to a phaser. Gets up. Fights. Gets his phaser knocked out of his hand. Falls again. Lands on the catwalk--no phaser! gets up. Continues the fight.
Then there's the huge long pipe to the drill-head beam. That didn't make any sense at all. Why not just phaser the cable? Oh, it is shielded? then how are people in thruster suits supposed to get onto it?
"Fencing." Fencing? Really. Since when does fencing involve a collapsible katana? "Kendo" or "Kenbutsu" would be the correct answer if you are going that route.
And that's what I remember off the top of my head.
So the whole thing about this being a reboot? No. If they had left out time travel entirely, and made the enemy be just the romulans testing out 2 new devices (cloak & plasma torpedo), which were defeated when Kirk Sr self-destructed to take out the mysterious attacker, that would have made more sense. Why the 20 year delay? Romulan high-command wasn't sure what happened, and decided to abandon the project. Then there was a change, and the Romulans decided to start building a fleet. Still want Nimoy in the movie? Let him be Sarek, or a member of the Vulcan Science Academy. Or a Romulan. Just anything else. (sure, there would be fans saying WTF, but it would have been better)
Trek always had flirting and kissing, but it was largely cute, relatively harmless (due to TV restrictions of the era). Not hot panting bodies covered in a shine of sweat. And it may have been intended as a joke, but the joke fell flat.
Trek has never been really good about time travel (except Guardian at the Gates of Forever), and really should stop. A completely alternate timeline would have been a better route to go, rather than the half-a##ed path of JJATrek.
Trek 4 was popular, but it was way too kitchy. They just wanted to make a funny movie, but the humor was way too dated (even when it came out), and it just wasn't going didn't work (for me). All you need from that movie is the first 10 minutes (where they agree to return home to face trial) and the last 10 (when the face trial, get the verdict, and the new ship).
Trek 5 was an abomination. Mainly because the studio kept insisting that they make the movie funnier, because that was what they perceived people liking about 4.