My favorite is people griping about how the Enterprise shouldn't look different. Yes, it should. The Kelvin might not have been the state-of-Starfleet-art, but it wasn't incapable of defending itself, and the Narada smashed it to pieces easily. That would make the Starfleet Corps of Engineers scrap the current plans for the Constitution-class starship and make her bigger and more powerful. Make the saucer, arguably the least vulnerable part of the ship, a bigger target, slim down the engineering section, beef up the dorsal neck, reduce the ship's over-all profile in many directions to present less of a target, and outfit her with more weapons. Not that hard to imagine.
I also didn't have a problem with "Bud-gineering" until I saw what they could've done if they'd had the budget for a set. I think and hope that they at least disguise the place a little more in the sequel.
"Geez, we've been back together for five minutes Doc, and you're already talking about the end of the universe."
"Stupid, stupid rat creatures!"