"Baby stalking" - what a great term. And no, I don't care if it's politically incorrect and apt to ruffle mothers' feathers. I have also witnessed this behaviour, albeit not the same extent as some of you (the monitor invasion story springs to mind). I react by giving such people the exact opposite of what they want: I blank them completely, and if I do make eye-contact, I look as disiniterested as possible. I hate the expectation that everyone within a 50-metre radius of a small child must coo and gush. If a child is behaving nicely and happens to smile at me, I'm happy to smile back - but I will not do it to stroke the mother's ego.
Sorry, the latest drama has made me feel a little defiant.