I had a really hard time today, while I was doing some groceries shopping. There was a Mom with a toddler and a 8 week old infant. She was jabbing along with a saleslady that offered samples. I took a glance at the baby, and she held her in the middle of her back, leaving her head in midair! her head was just half-hanging there..
I had to use every restraint to not ask her if she was stupid or just wanted to damage her daughter's neck..
This stuff drives me CRAZY!! 
Re: Keeping calm while seing other moms!
I don't mean this lightly, but sometimes it's easy to spot a second or third-time mom, LOL.
The other day my coworker (who has a little guy a few weeks older than our kiddos) was in with her 4-week-old. When she went to hand her off to another coworker to hold, we all joked you could tell this baby was her 2nd. With E she would hold his neck, lightly place him in the person's arms, shush, etc. With Z she just reached out and sorta dropped her in our coworker's arms.
It is so hard.
In a way I am less judgey of moms/kids than I used to be. I used to be one of those that got annoyed when kids we causing a scene or being annoying. Now I just give the momma a look of understanding and feel for her. I've been there, am still there often LOL.
Though I am also 100 times more judgey of parents that are putting their child at risk in some way. It makes my blood boil.