Should you list irrelevant work experience on graduate school applications?
1) If we're asking, we want to know. It's fine to list workplaces that seem irrelevant -- for the (professional) graduate program I teach in, a little workplace seasoning is a distinct plus no matter how connected it is to the program. Moreover, some of our applicants are surprised by the variety of experiences we find relevant. (Retail? You bet. Sales? Absolutely. Office temping? We won't have to teach you what a memo is, good.) So yes, it's "permissible" to leave these jobs out, but you're more likely to hurt than help yourself thereby.

2) Rule of thumb: if you wouldn't put it on your résumé, we don't need to know about it. If you babysit regularly enough that you have certifications and know CPR, sure, tell us about that. Help out the neighbors with their kids occasionally? We don't need to know, and we'll suspect that you're trying to pad your application.