It was a great movie and an excellent finish to the trilogy.
Most movie franchises have utterly tanked by the third sequel but this was really well-written, well-executed and it never slowed down for an instant. As usual I laughed at Will Smith's timing and reaction shots through the entire flick, he was very funny. Josh Brolin was excellent as a younger version of Tommy Lee Jones and Jemaine Clement as the villain.
I have not seen a film I enjoyed this much since Men In Black II. I wish Hollywood did more flicks that did not take themselves too seriously and were designed for you to be able to take your family to them without wincing at every other scene. The reason I always liked the Men in Black films is that they seemed to be aimed at kids without intending to brainwash them or propagandize them. I was really stunned when the movie ended and I realized there were no gay porn sequences or shots of men kissing at any point. That is very surprising nowadays.
If you ever wondered what exactly it was about Jay that caused them to recruit him, you will find out in this film at the end. Cleverly wraps the whole thing up.
Some people have complained about the wild absurdity of the aliens and the premise, suggesting it is designed to break down the brain's ability to discriminate between dangerous and safe but I would posit that this is really a tradition in science fiction, this would be one of the few movies that conveyed the madcap nature of the universe depicted in the Golden Age of Science Fiction. The films have tried to depict the cosmos as so wonderful and so bizarre that our minds have to filter most of it out - and I always enjoyed that take on the world.