It is clear that what the machine operators tell Montag about the high incidence of attempted suicide attempts reveals the way in which the dumbed down form of society that the novel presents us with, where books are illegal and citizens are encouraged to engage in forms of entertainment that only serve to expose the emptiness and meaninglessness of their lives, is resulting in people lacking lives of depth, significance and meaning. Note what the operator says:
We get these cases nine or ten a night. Got so many, starting a few years ago, we had the special machines built. With the optical lens fo course, that was new; the rest is ancient. You don't need an M. D., case like this; all you need it two handymen, clean up the problem in half an hour.
The suicide attempts are clearly linked to the changes in society, and the fact that they get so many "cases" like this every single night that they have had to invent new machines to cope with it points towards the deep unhappiness of so many of the populace. The case of Mildred is obviously the norm rather than the exception.
That overdoses are a common occurrence in the society of Fahrenheit 451 is significant because it suggests that people are unhappy. Remember that this society is obsessed with leisure and entertainment: people watch the parlor walls constantly, drive too fast on the highway and go to specially-designed Fun Parks. Moreover, the banning of books means that they do not have to think for themselves; they simply enjoy the less serious pursuits of life.
It is significant, then, that people have unbridled access to all of these leisure opportunities and still decide to take an overdose. It proves that entertainment is not the cause of happiness and that, in fact, it may be a contributing factor to depression and unhappiness.
This fact about the number of overdoses reveals the book's central irony: that learning is not the source of unhappiness, as this society so strongly believes. In truth, it is only when we are deprived of books and education that we experience misery and upset.