The technician tells Montag that cases like Mildred's are extremely common. What does this indicate about the state of Montag's society?
I agree with the previous answer's assessment that there isn't one correct answer to your question.
The technician says that overdosing on sleeping pills is quite common, which indicates some very concrete details about the society. First, sleeping pills must be very common among the general population. If lots of people are overdosing on them, then lots of people have them. How are they getting them? Doctors might be prescribing them left and right as an attempted cure all for people's ailments or depression. It's possible that sleeping pills are no longer a prescription med. People can simply buy them over the counter, which makes them convenient and cheap.
Why might people need so many sleeping pills? I like the previous answer, and I'll attempt to add some to it, but first I want to stay concrete and go for a biological reason. People are taking sleeping pills, because they are not falling asleep easily. That sounds lame, I know; bear with me. A big part of being able to fall asleep easily is exercise. I've attached a link below to a short article about sleep and exercise, but the first line states it in simple words for the reader.
"People sleep significantly better and feel more alert during the day if they get at least 150 minutes of exercise a week, a new study concludes."
I'm quite certain that Mildred doesn't get any exercise. She stays at home with her 3 walls of TV family. She doesn't do that once or twice per week, but every day.
Another reason that people in Montag's society might not be falling asleep quickly, and therefore gobbling down sleeping pills like candy, could be the screen time itself. Many studies have been done about how TV/phone/computer screens delay sleep cycles, because they trick our bodies into thinking that it isn't night time. That delays the release of melatonin, which is your body's natural "sleepy time" hormone. Mildred is constantly being bombarded with screen time, which almost assuredly suppresses her malatonin release. That throws off her body's natural circadian rhythm; therefore, not allowing her to fall asleep at bedtime. What to do? Take a bunch of pills. Bradbury makes it clear that Mildred is not odd in her habits. Mildred is the norm, which explains the technician's comment.
The above are just some of the biological issues that Montag's society might be experiencing. That doesn't even scratch the surface of the psychological reasons Mildred and other people are taking sleeping pills for. The above answer (Nolan McShea) did a nice job of explaining the sheer depression that Mildred and others might be experiencing because their lives don't have any personal meaning. Mildred is empty herself because the only thing she fills herself with is the hollow and meaningless lives of TV people. She doesn't want to feel empty, so she takes a bunch of pills in order to feel nothing.
Maybe the convenience of the sleeping pills is a government ploy to keep people easily under control. If the only thing your citizens are doing is watching TV and passing out from sleeping pills, they aren't really doing anything wrong. They aren't "awake" enough to question anything the government says or does. That fits with the novel, since the entire point of burning books is to stop people from asking questions and thinking for themselves.
Ah, the irony of Fahrenheit 451. A book about a world without books where firemen use fire.
I personally do not think there is a correct answer to this question. You can look at this from several perspectives.
Mildred nearly kills herself from an overdose of pills. Why so? You could simply say that she forgot about taking pills earlier, and that she accidentally took more than she should have.
However, it is questionable that that is the case. Although Mildred seems to have a pretty comfortable life, watching television and socializing with her friends, there is nothing that shows what she really feels. We can all pretty much say that the society Montag lives in is pretty depressing. It is a society where happiness is to show, but yet there resides no actual happiness. So, possibly, this is what Mildred felt; this dread of unhappiness and the unnatural feeling of denying her true emotion. Therefore, she attempted to escape it all by taking those pills.
So, answering the question itself, the evidence shows that Mildred is very depressed. If the technician says that these cases are extremely common, the chances of these overdoses being the effect of depression, it is certain that the society that Montag lives in is an absolutely depressing society.
As I mentioned before, the society he lives in seems good for the looks; everyone seems to be happy, the civilization seems as if it is thriving. However, due to all of this "denying happiness," this shows that this is the society no one would like to live in.
I hope I helped!
Fun fact (in case you didn't know): Fahrenheit 451 is the name of the book. Why? That is because 451° is the temperature where paper starts to burn; thus, the paper of a book!