the movie revolves around a hero -- a concept that Rand greatly lauded over the muddy protagonists of most modern work. Mr. Incredible is by no means flawless, but he is shown to be exceptional in a world of mediocrity, as are the movie's other superheroes.
Well, sure. Rand's followers like to rail against mediocrity, but of course this is a huge strawman -- does anyone going around defending mediocrity and conformity? Okay, maybe Rousseau, but he also says a community ought to try to kill everyone who's not part of it. Certainly you don't find this in any serious social/political or ethical philosopher of the nineteenth or twentieth centuries (fascist paeans to the glory of a totalitarian state don't count as serious philosophy because they're not). Even Marx's (in)famous dictum starts with the clause `From each according to his ability'.
On its flip-side, the movie's villain is also a classic Objectivist foil. Voiced expertly by Jason Lee, Syndrome is everything that Rand deplored in her novels -- a conniving, manipulative man who seeks personal gain without honest work or achievement.
Well, er, no. Certainly Syndrome is conniving and manipulative and seeks personal gain at the expense of others, but he works even harder than the Supers to get his power -- he's born with nothing more than a genius for invention, not special abilities, and spends fifteen years building his fortune and developing his weapons. He conducts himself with an utter lack of respect for those he perceives as his inferiors (that is, everyone else), but, in Rand's ethics, that's a virtue of the superior, not a vice.
What's more, consider Rand's 'heroic' character Howard Roark, who destroys a building, killing the people inside, to keep others from taking credit for his work. Does this sound more like the altruistic and self-sacrificing Supers, or Syndome's plan to gain fame by launching a giant robot at the city and pretending to defeat it in battle? (Not to mention Syndrome's fit when the people he's 'rescuing' mistake him for some of the old Supers.)
Certainly The Incredibles calls on us to celebrate and develop our natural talents. But the heroes of the film develop their talents in pursuit of the greater good and classical notions of duty and virtue, not out of Rand's twisted ideal of self-aggrandizement no matter the cost to others. If anything, The Incredibles is an anti-Objectivist film.