First of all, I really cannot stress more that you should really read the Watchmen book.
OK here's my stab at this question. There are a lot of differences between the book and the movie, and if I was to use a term to collectively describe these differences I would say narration density. Watchmen is a rather dense book that effectively uses it's panels to tell several tangential stories. That's very hard for the film medium to achieve. Let's take a look at a simple panel:
Here we have a meeting of the Minutemen, the previous generation of superheroes in the Watchmen universe. In this one panel we can see all of the Minutemen. Not only that, we can see them interact. Captain Metropolis is being the obvious host, the rough and tumble relationship between Comedian and Sally Jupiter (foreshadow!), Hooded Justice observing the two or perhaps observing Captain Metropolis (more foreshadowing!), the first Nite Owl jovially ordering prints, and Silhouette being her lone wolf self. In the corner we see a newspaper with the headline "Scientists make first artificial wonder element: Plutonium".
So with one single panel we established the team and their dynamic and also put a date on this encounter. Putting that much storytelling in film would cost several precious minutes. And even then a lot of the details would be considered "Easter eggs" that most people don't notice. In contrast, the panel is just there. It's not going anywhere. You can stay on it, read it, enjoy it's art, analyze it's components, and it would still be waiting for you. No clumsy pause button required.
It is this single - very important - quality that is unique to the graphic novel form which drives all the changes the transition to a movie required:
"The Tales of the Black Freighter" was cut. Even disregarding screen time issues, this comic within a comic would probably pose an insurmountable challenge to incorporate in the film in a way that wasn't too jarring and clumsy. While it is not that important plot-wise, it does help set the atmosphere of impending doom in the book and provides an eerie parallel to the main story.
Most of the background history of the characters was cut. Most of the Minutemen's story was condensed into the titles montage (which I actually enjoyed), so we lose some of the sense of history between the characters. Little things like the Nite Owl I writing a book about the Minutemen (and his ultimate fate) all give the characters a bit more dimension.
The ending got changed. Without revealing too much about the comic book ending I'll say this: changing the ending was a wise choice. The original ending was the culmination of a secret conspiracy that was building up from the very beginning of the story. Countless little details, scattered in the corners of panels, foreshadowed it's coming. Doing that in a film medium, without making it look like a Deus Ex Machina, would've required an inordinate amount of time.
Several minor, throwaway, characters got cut. A recurring scene in the books is the Newspaper seller's stand. The cast of characters featured in those panels are mostly unnamed. Yet through their interactions and their panels Moore establishes atmosphere and drops hints on what is to come. You cannot do that easily in a film medium.
I'd like to close by saying that despite it's flaws, I really did enjoy the movie version of Watchmen. It was as loyal to the original story as it can be (a bit too loyal some might argue) given the obstacles in front of it. But if anything, its flaws only reinforce Moore's assertions about the major differences between the two mediums.
