When it comes to the Tech of the reboot, my only problems are pretty much personal opinion on the visuals (the Enterprise itself looks horrible, or the bridge is stupid, for example) and some problems with the logic of the stuff, like
why is there a giant window on the bridge? Doesn't that make it easier for all the bridge crew to get pulled out into space?
Why are there so many pipes in main engineering? Is it steam powered? (I know why it is like that from a real world standpoint, but I'd like to hear a good in universe explination)
What is the purpose of the lens flare generators? (this question is phrased sarcastically, I know there wasn't supposed to be lens flare generators on the ship, I would just like to know what idiot thought constant lens flares was good).
(I'm not actually asking those questions expecting to get answers here, they're just examples of some of my problems from a tech/visual standpoint)
But, as much as I like the tech of ST, I could have ignored it. With the reboot, its the story/writing/acting that gets my undying hate. I don't hate the movie because the Enterprise is different, I hate it because it sucks (same with the reboot ship itself, if it looked good, I'd acknowledge that it looked good). The tech annoyances are just that, annoyances. I've never had a problem with stuff like that, or minor continuity mistakes/fixes in the shows (although I'm a big fan of continuity in general).