It can go the other way, too. Parents can miss a lot, simply because they're around their kids all day.

I remember being on an airplane with a mother and her toddler; the little boy was crying desperately "I wanna go to the BATHROOM!" while the mother was doing everything to calm him but taking him to the bathroom. I think, being frazzled, she must have just perceived as wordless screaming what I clearly understood as words.

Even stranger example of this: when I was about six months old, my mother made a cassette tape of my "baby talk." Years later she listened to the tape: and I wasn't babbling, I was speaking understandable words. Under the stress of caring for a small child, you don't actually notice details that are obvious to a non-parent observer.