• Kirk and Scotty both use minor foul language. Star Trek IV: The Voyage Home established that foul language was archaic in Kirk's time. Kirk was so unaccustomed to it that one of his attempts of using it was the clumsy "Well, a double dumb ass on you!"
• The shields do nothing. Ok, I can accept that weapons from a future ship could pass straight through the defensive shields of the Kelvin and the Enterprise. Debris, however, should bounce off the shields and not get close to the Enterprise's hull. Likewise, dust in Titan's atmosphere shouldn't spill off of the hull; the deflector shield would've formed a bubble around the ship.
• Where are the planetary defenses? Vulcan and Earth rely on starships to save the day. How about terrestrial and orbital weapons? Space platforms? Ships local to the solar systems?
• The number of Vulcan survivors is low. Vulcans were a space-faring race long before they made first contact with Earth. The show Enterprise established that they had outposts and a significant fleet. Thus, many Vulcans would've been off-planet.
• Delta Vega shouldn't be anywhere near Vulcan.
Of course, the number of references and homages to original Star Trek greatly outnumber these nitpicks. I'll leave geekier people to compile them all.