In a recent post, Mark refers to "Arnold Zwicky, who is at home on babysitting duty". Forgive me airing a pet terminological peeve, but especially with Father's Day coming up: Arnold is not babysitting if he's looking after his own kid(s). In the relevant sense (versus, say, tending a neighbor's plants or keeping an out-of-town visitor entertained), the term refers to "the work of a baby sitter; caring for children when their parents are not home" (WordNet), or caring "for children usually during a short absence of the parents" (Merriam-Webster online). Unless he's looking after someone else's children in his house, my word for what Arnold is doing is parenting.
[UPDATE: Oops. Mark informs me that Arnold was indeed watching someone's child other than his own (who is about 30), and used the term himself (quite appropriately). My button-pushed reaction comes from having heard "I'm babysitting" used by quite a few recent fathers I know, which always makes me wonder how much they're being paid and who they're supposed to call in an emergency.]