Minor Plot hole: In the movie, Red Matter can create black holes, but can also create time-traveling holes; depending on what the script needs. Also, a drop of red matter or the entire ship supply will cause approximately the same effects.
Minor Plot hole: When a black hole is created inside Vulcan, the small planet that is close enough for Older Spock to see his home planet disappear does not get drawn towards the black hole.
Minor Plot hole: Captain Robau accepts to meet Captain Nero at the beginning of the movie in his ship. The technology that permitted them to talk in their respective cockpit was enough to have a fluid discussion. There was no good reason for Captain Robau to leave his ship and to board Nero's in order to have a conversation he could easily have in his cockpit with the added bonus of being protected from stab wounds.
Major Plot hole: Because Kirk is challenging the authority of Captain Spock, he is marooned on a dangerous icy planet....instead of being kept in the Enterprise in a cell. Which is surprising considering that most of Star Fleet was destroyed by Nero. Who would pick Kirk up ?
Major Plot hole: A Supernova is not a surprise. it announces its arrival millions of years in advance. There is no reason for all Romulans to die to a Supernova when primitive humans of the 21st century can already know when a star will die.
Plot contrivance: In Star Fleet, 90% of the personnel are students (that makes sense), most of which die during the attack on Vulcan; and no one seems to care afterward.
Plot contrivance: Chekov is able to find and beam Kirk and Sulu in the Enterprise while they fall from the sky but is not able to beam Spock's mother that is right beside all the other Vulcans who get beamed successfully...just because the rocks under her starts to fall.
Plot contrivance: Kirk, who could have ended anywhere on the Icy planet (Delta Vega), encounters the older Spock just before he is killed by a terrible monster. The odds of Kirk's capsule landing a couple of meters away from Spock's cave are ridiculously low.
Plot contrivance: Apparently Old Spock must have been able to manipulate the laws of physics to be able to witness Vulcan's destruction by a black hole with the naked eye instead of, you know, being sucked towards the black hole himself and die with icy adjacent planet.
Unaddressed Issue: Nero, the villain, comes back in time. During the whole movie, he seems dedicated to keep his operations limited to his star ship. Did he contact the other Romulans to tell them that their planet will explode in a century ? Since they failed to notice it themselves, it might have been important for someone to eventually contact them.