There are similarities in this novel to all societies, as part of what Bradbury writes about is human nature: the need to feel secure, the tendency not to question or critically think. The US tends to swing on a pendulum over time between a society that is quite free to one that, in a limited way, more closely resembles the society in the novel. I think the main similarity I can see is the social pressure not to question our wars, or to criticize government decisions.
I think it is very similar, too, the way that Mildred is in the book compared to people today. Remember when she wants to surround herself with her tv screens so she can be surrounded by the characters she has come to know and love? She considers them to be like real people, and as such she has no real need for significant human interaction. Think about how people today are always surrounded by screens, from televisions to video games to cell phones and MP3 players. Mildred buys into the message put out by her television screens without question. How many of us do the same thing?
There are many similarities between the society in the book, "Fahrenheit 451" and today's world. In the first part, Clarisse tells Montag says everyone wants to go so fast. She tells him that billboards are 200 feet long because cars go by so fast, that the extra length is needed so people can read the billboards. Our society likes speed, too. When Capt. Beatty, at Montag's house, talks to him about their society, he says that people wanted increasingly shorter bits of information, so books were condensed and became bland. Our world loves the "sound bite"; the quick video of a news item. Beatty also talks about political correctness and how that made writers and publishers take out anything deemed offensive to any group. Being "PC" is very important in our world today. "Merry Christmas" has become "Happy Holidays" for that reason. The schools in the book's society concentrate more on sports than on education, we're told. Many schools now do the same. Beatty tells Montag that people want to be entertained and they want it immediately. We pay people who entertain us huge sums of money while those who protect us and teach us are on the lower rungs of the pay scales. We want faster and faster forms of communication in our world - the faster, the better. Also - far too few people read books anymore. Bradbury said to destroy a culture, get people to stop reading books. I see that happening.