Mildred is Montag's wife. She doesn't work; she doesn't have children; and, she doesn't do anything productive all day long. She is the typical hedonist citizen who lives a completely distracted life. She loves to watch her three TV walls, sleep with her radio Seashells in her ears, and drive her car so fast that she kills dogs. If that wasn't enough to be wrong with Mildred, she also takes sleeping pills like they are candy.
Montag comes home late from work one night and finds his wife completely unresponsive. When he calls the emergency number, a couple of technicians arrive with a stomach-pumping machine to save her. Montag asks why a real medical doctor wasn't dispatched and the men say that they have so many calls each night that the medical field created the mobile pumping machine to take care of everyone. This is significant because Mildred's problems with sleeping pills and her way of life in general reflects the populace as a whole. When Mildred is better, and Montag feels it is a good time to talk about her almost dying, she completely denies having taken too many pills and the discussion ends. Either she really didn't know what was going on, or she doesn't care that she almost died. Both possibilities are terrifying.
Physically, the main thing that goes wrong with Mildred in Part One of the book is that she almost dies. She accidentally takes a whole bottle full of sleeping pills and is near death before Guy gets these guys to come over and pump her stomach and replace her blood.
But you also have to wonder why this happened, because that tells us (I think) what is really wrong with Millie. What is wrong is that she is really not happy. She has no emotional fulfillment in her life because all she cares about is the "families" on the parlor walls. This is, Bradbury implies, why she has allowed herself to make the "mistake" that almost kills her.