The story: What can I say? The similarities are name, demigods and that's pretty much it. There isn't much thats the same as the book. The story on its own works decently for a movie. Their on a quest to save his mother and he needs three items to be able to do so. So the quest begins. I'm not going to harp on the differences, but as the story goes for the movie, it was pretty straight forward and simple to follow. Some of the action pieces were well done as well as I felt the special effects served their purposes. I would have liked more development of the bad guy as it sort of comes out of nowhere how he's revealed and such, so when it happens it seems a bit bland.
The characters: I felt that the three main characters were very stereotypical teenagers. The smart and feisty girl. The mack daddy kid and the brooding main character. There wasn't enough depth to really care about what happened to either of them. I think they did this to cater to the audience as Grover came across as comical at times, but more childish comedy than any substance behind the stuff he does. The relationship that the main character explores with Annabeth seems sort of odd in the movie because they are enemies then all of a sudden they are close. There isn't any sort of transition between the two points. The minor characters were that, minor. Nothing notable about them besides their Greek Mythology reference.
The overall feeling of the movie was a cheap cash-in on the success of the book. I liked the idea and if adapted more true to the book it would have been a better story. Overall it came across with very little of the charm and magic that the book held which was too bad. I honestly think they will make the sequels, but don't know how they will fit in with the other books as some of the main things that are carried over in the rest of the books are omitted from the movie. I would give this movie a 5 out 10. A good movie if you can look at separate from the book, not so much if you are comparing them.