Like the movie that inspired the show, Agent K and Agent J are the main characters. Since the movie felt almost like a cartoon (with cartoony violence and wild stunts) the transition from live action to cartoon is actually quite smooth. As far as continuity, the cartoon picks up from the first movie, only it's somewhere before K has had his memory wiped at the end of the movie since in the cartoon series he's still an active agent. There are other changes as well such as Zed's appearance. Only true MiB continuity buffs would be concerned about these but for me they didn't impede my enjoyment of the show in the slightest.
In many ways, the cartoon comes across as being more serious than the movie. The titles sequence is one good example. Use of "lighting" techniques and "time lapse" photography as well as a steady beat that the characters all move to gives it a very serious (but stimulating) tone. In many cases, the color pallet is kept very dull. Your main characters are dressed all in black and often the backgrounds are plain grey or dull greens.
The action sequences are very similar to the movie- over the top, cartoony violence in which nobody ever really gets hurt. There are some pretty weird and gross sequences that were surprisingly graphic, such as aliens bloodlessly bursting out of human bodies.
I'd say they nailed the characters' personalities. K is the all-knowing mentor who plays his cards close to his chest (a series-running gag is K's apparent demise proving false). J is overconfident know-nothing who constantly makes a buffoon out of himself. By the end of season four, however, you're wondering why J hasn't improved his skills and increased his knowledge. It was interesting for me to be introduced to other agents and to more fully explore the history and inner workings of the MiB over the course of the series.
Overall, the series nails the tone and mood of the movie. The slightly insane logic that rules the galaxy is well applied. The episodes do tend to all blur together, however. With few exceptions (such as Alpha), the villains are pretty much totally exchangeable. They get used for one episode and then are never seen again. The show's running gags such as the word "Syndrome" in all of the titles do wear a little thin and serve to make the series even more predictable than it already was.
Basically, your reaction to this show is going to be the same as your reaction to the movies.
1LR Review - 13 out of 20! It's a Glancing Hit!