With that said I'll start with the good. Karl Urban's Dr. McCoy was the one shining star in the film. His deadpan line, "He'd let you die Jim" was perfect. It showed the struggle between compassion and logic that was so well portrayed by Kelly and Nimoy in the original series.
First, the film completely disregards Star Trek cannon. Christopher Pike does not live through the movie to end up as a quadriplegic on Talos IV. The Klingon home world, Kronos, appears to have a moon, Praxis, that has exploded, except this doesn't happen until Star Trek VI. All this is forgivable however; new movies for a new generation that knows nothing about Star Trek
Second, what isn't forgivable is that basic Newtonian physics and science is so poorly understood by the film makers that it distracts from the movie. Some examples of plainly not understand that the world around you is governed by science and not magic are: the heat from the volcano is attributed to damaging shuttle craft Galileo yet the heat caused by de-orbiting the shuttle craft would far exceed any heat caused by a volcano. In the same sequence, the Enterprise is parked underwater. Are we to believe that a star ship that must be constructed in space and is designed to be used for interstellar travel also doubles as a submarine? When was the last time that you boarded a 747 to go on an undersea adventure? And why in the hell would they park the Enterprise underwater when they could be invisible in orbit directly above the volcano and use sensors and transporters?
Other big issues are that the crew of the starship Enterprise does not know the distance of the moon's orbit. Ask Neil Armstrong, I bet he figured it out 300 years earlier. I think the first question on starship helmsman's exam should be, "Where is the moon and so you don't hit it?" Next when the ship can no longer hold orbit, it falls back to earth in a few minutes like a stone dropped into a pond. Newton? Never heard of him! What laws of motion? I think movies reflect a lot upon a generation. This new generation claims nerds are cool, but has no manned space program. Your parents' generation actually walked on the moon.
Third, when the script however fails to make common sense, it throws you outside the movie and this makes the movie 'unfun'. After a secure, secret Starfleet facility is attacked, Starfleet Command decides to meet in an unprotected high rise. I guess in the 23rd century, rank isn't correlated with intelligence or experience. Next, the Klingons are a war like race equally as advanced as humans that have developed space travel but they don't bother to guard their entire home world. They actually sound pretty easy to conquer. That's okay because humans are just as dumb; two Federation ships appear in earth orbit to duke it out and there are no other Federation ships around. Please, will one ship randomly fall on San Francisco? We sound pretty easy to conquer too.
Let's not forget about the unnecessary, obligatory, giant tittied girl in skimpy underwear to make all the 14 year old boys have happy wet dreams. I love nude women as much as the next guy but porn has it's time and place and this wasn't it Unless you are a 14 year old boy with $10.50 for a movie and no other access to porn.
When Kirk died, why did Dr. McCoy need Kahn's blood to save him? He had 72 genetically engineered humans from the eugenics war frozen in front of him. The Eugenics Wars are well documented. He actually had to thaw one of those guys out to put Kirk in the life support tube. Why not use his blood or one of the other 71 samples of super blood?
Fourth, I remember when Spock died in Star Trek II, people cried, it was debated if he could really be dead. It was an emotional heartfelt moment that asked the audience to way, "the needs of the many, versus the needs of the few." Did anyone really think Jim was dead in this movie? He was dead for all of five minutes! It was a completely wasted scene because it was devoid of emotional connection. I believe it was 30 seconds wedged in the middle of two action sequences. This may be because modern movie audiences lack the social skills such as empathy which are necessary for bonding with others. So the film makers simply recreate a scene from the past devoid of emotion and the audience believes it has the received the same spellbinding moment that their parents received.
The only emotion portrayed in the whole film is the Caulfield like teenage angst of Captain Kirk. Great men are no longer portrayed as being challenged with great responsibility or moral questions but now face the pubescent problems of spoiled teenagers. This is the greatest reason why this new Star Trek movie fails. Gene Roddenberry created a future where men had moved beyond many of humanities vices. He created a series of moral plays in his "Wagon train to the sky"; the original series is more like twilight zone episodes than anything else. Where in this movie did you feel good about humanity? Did this movie make you feel like we could end the Iraq War? That's how the old series made you feel about Vietnam and the Cold War. Did it make you feel that bigotry toward gays would end? That's how the original series made you feel about racism. The movie is an epic fail that reflects a generation that is an epic failure.