First of all, the storyline is incredibly deep, and the characters are so remarkably layered, which is rare for an animated family film. Just think about it - the main plot revolves around a super hero's midlife crisis and how it affects his family. (You could almost say it's a family-friendly version of "American Beauty" with superheroes and a happy ending. Sort of.) Beyond that, however, the film paints the very complex portraits of several relationships, and the people within them.
Bob and Helen Parr (AKA Mr. Incredible and Elastigirl) are dealing with the trials of marriage, while their children have to deal with being repressed superheroes growing up in a dysfunctional family. The villain, Syndrome, was once a naive child whose entire outlook on superherodom was destroyed, disillusioning him to the point of becoming a super villain. His relationship with his proposed lover, Mirage, is also shown as being extremely strained (it's a small moment, but we learn so much after he doesn't attempt to save her from Mr. Incredible).
On a technical level, the animation is noticeably not as advanced as current Pixar films. However, the animators make some wonderful achievements. One feature of the film is the unbelievable expressiveness that is displayed by the character's eyes and body motions. In a live action film, the small touches of an actor can express so much - thankfully, Brad Bird did not let his medium limit his power to convey emotions that way. So many times (especially with Mirage and Mrs. Incredible) the expression shown through the characters could rival the performance of a live actor.
Finally, the voice acting is some of the best in a long time. Pixar films always have great vocal performances, but you'd be hard pressed to find better than this. Holly Hunter, especially, does great, emotional work that transcends the barrier of the medium to create affecting work. Brad Bird himself is hysterically memorable as Edna Mode, and I was surprised to find out that Sarah Vowell, frequent This American Life contributor, provides the voice for Violet, which I love.
Of course, on multiple viewings, the flaws of a film start to come through as well. There are a few plot holes, and admittedly disturbing moments (is...Dash...killing those people...and enjoying it? He's just a little kid!). But they are so, so small and insignificant that they are easily dwarfed by the spectacular achievements the film reaches. Like most of Pixar's releases, "The Incredibles" was a revolutionary film that resonates even more powerfully on repeat viewings.
How do you feel about The Incredibles? Am I thinking into this too deeply, or am I spot on? Comment BELOW!