So, in the case of the OP's story, the fact that the mother kept going on and on and not caring that other people were staring and even reacting shows that its more than likely a common occurrence. She doesnt have the natural shame that should rear its head in a situation like that. In the personal stories PPs have shared there is the common theme of saying a few words or sentences, feeling bad either because of other people's reactions or simply because of natural shame and then not repeating the behavior. You see the difference? They probably also didnt have an even tone since they're not used to speaking that way, and their child probably reacts strongly to the words, crying loudly or screaming or another form of acting out. In the case of the child the OP talked about, it sounds like he was crying quietly and trying to disappear--a clear sign that he is used to the abuse.
Maybe its clearer to me because of working in the public around kids for several years, so i have enough experience to notice the differences. When I think about it, though, i think it has more to do with trusting my instincts. I'm not afraid to go with my gut reaction and notice how something makes me feel on an intuitive level. OP, it sounds like you're afraid of trusting your own instincts and feelings, for the sake of not being "judgmental" (you even used that term when it comes to assessing the situation, which shows how scared you are of doing it). The only way to truly know how to react is by listening to yourself, which means you need to be willing to step out of the neutral zone, stop feeling afraid of judging, so that your true feelings and instincts can shine through. If you're constantly uptight then you're not going to be able to trust yourself. Trusting your instincts is very important in a case like this because you will be better able to assess if it would be good to try to distract the mother or help her feel better so she stops hurting her kid or leaving the situation alone since you've assessed that this is more than likely a common occurrence. You can also be able to assess if you should call the authorities or not.