How does government control of the people in the book relate to today?
Another important aspect of government control in the novel is how it came to be, and that relates closely to our society today. In Part One, when Beatty goes to see Montag, he spends a good deal of time explaining how their current laws originated, and while there are some aspects of his explanation that lack credibility (i.e. the history of the fire service) there's nothing to contradict society's role in its ready submission. Government control came about through the will of the majority, and the intellects went underground to protect themselves. The political correctness that led to the Fahrenheit 451 society glimmers within our own, and more and more it seems as though people are afraid to take a stand against the government, or when they do, they are easily cowed back into submission and issue a public apology. Thus, just as Bradbury's hyperbolic society gave the control to the government in order to simulate some form of happiness, our society seems to be following a similar path, though more realistic.
Ah, a fun question! The government control in this book relates directly but not intensely, at least unless you include the entertainment industry. By that I mean, the government keeps strict track of what is read and what books are sold in this novel, guiding people away from deep and revolutionary thoughts. That's not really what's happening here and now. Any book can be sold, and often is. However, the government does track media for subversive activities, which is related—and the media contributes to both forms of control via overwhelming distraction. Think of the fact that more people vote for American Idol than in some presidential elections and you'll get a sense of what I mean. (At least, more votes are cast.) Also, on a different note, the government is working on robot warriors that would parallel the hounds in the novel, and developing non-lethal weapons that relate to some of the chemicals used.
It all depends on your perspective and what you consider the government's motives to be. If you look at our public education system and the fact that it ends up discouraging reading and often tells students how they ought to think about certain books and which ones are worth reading, you can make the argument that the government isn't all that far off from the one in the book.
The entertainment industry is not an arm of the government, however, or at least not in anyone's mind except the most ardent conspiracy theorists, so it is hard to square it with the way that elections and whatnot are staged in the book. But it certainly plays a role in "dumbing" things down, again depending on your perspective.