What are the evidences that the society is fixated on materialism and doesn't understand itself in Fahrenheit 451?
The people in the dystopia of Fahrenheit 451 are consumers of materialism: they burn books, overdose on drugs, watch TV non-stop, and use helicopters and mechanical hounds to spy on and kill people.
In Part II "The Sieve and the Sand" Captain Beatty says:
The books are to remind us what asses and fools we are. They're Caesar's praetorian guard, whispering as the parade roars down the avenue, 'Remember, Caesar, thou art mortal.' Most of us can't rush around, talk to everyone, know all the cities of the world, we haven't time, money or that many friends. The things you're looking for, Montag, are in the world, but the only way the average chap will ever see ninety-nine per cent of them is in a book. Don't ask for guarantees. And don't look to be saved in any one thing, person, machine, or library. Do your own bit of saving, and if you drown, at least die knowing you were headed for shore. (86)
Books stand in sharp contrast to materialism. First, they are comprised of ideas, and they lead to asceticism (the holy life). The Book People are like the prophets and disciples in the scriptures: they are common men who live outside society by humble means for a higher cause. Other martyrs, like Clarisse and the woman who burned herself, refuse to base their lives on material items; instead, they live by the light of knowledge taken from books. Gradually, Montag learns from their examples.
Beatty says that the "The things you're looking for, Montag, are in the world." The dystopia of F451 is based on worldly items: houses, wall screens, drugs, sex, and money. Beatty tempts Montag here the way Satan tempted Christ: with bread (hunger for wants, desires, things).
I would say that the best evidence of both of these problems can be seen in the character of Millie Montag.
Millie is the character that we see who is most clearly fixated on material things. It seems like all she can think about is getting that fourth parlour wall put in so that she can spend more time with her "families" in the shows that come on the parlour walls. She does not really care about anything other than the walls and the "people" who she sees on them.
As far as not understanding themselves, she exemplifies that as well. She is so clueless about herself that she does not even realize that she took the overdose of sleeping pills and almost died. We can see that many people in the society are just like that because one of the men who pumped her stomach out said that they had lots of people who needed to be saved in that way. To me, that indicates that many of the people think they are happy but don't understand that they are really very depressed.