Perhaps the most interesting thing about this thread is that people assume that us parents just don't care if our kids annoy others.
The fact is that the parents on board your flight have probably thought more about how to get through that flight than any other pax on board. This would be true regardless of the length or time of the flight. Us parents will typically have thought up Plan A, Plan B and Plan C. We'd have thought about ways we can distract our kids in both the airport and once on board. We'd have double checked that the children's favourite toy (of the hour) has come along and that it's suitable for use on an airplane (are you non-parents even aware how many toys these days make noise and can't be turned off?), we'll have various snacks, and devices and comforts from home. We'll often even forgo our own comfort and entertainment, all to try and make everyone else's journey pleasant.
The thing is kids are not miniature adults. As mature as some kids can appear, they are still kids and have the reasoning ability of kids. So the idea that someone would come up to me and make comments (before anything had even happened) is downright offensive.
Furthermore, if a kids gets into such a state, there is every chance that us parents are acutely aware. The kids might have reasoning ability of kids, but us parents still feel the weight of society judging us come down on us like a ton of bricks. However remember that kids can also be sneaky. They may try to do something and ensure their parents don't notice. So sometimes the answer to the question of "did you know your child was doing X" is in fact "No, I didn't, because they are a sneaky little cough".
To give you an idea of the sorts of stuff that can make a kid have a meltdown, I once spent 2 hours of a 9 hour flight trying to convince my son that I can help him with the tray table because he couldn't get it to stay up. I've had my daughter get upset because we'd been stuck on the ground for an hour, and I've had my other daughter get overtired on a flight which left at 11pm at night (like all LAX - AU flights do)
Finally, everyone remembers that one flight that they have been on where the baby wouldn't stop crying, or the child would play with the lights and call attendant button or they would kick the seat in front. But most people have forgotten the likely hundreds of flights were they where not even aware there was a kid on-board.