One of our Park Slope GL operatives sent along this question, which has made the rounds via the always compelling, and widely circulated, Park Slope Parents email list:

A friend pointed out to me yesterday that the word “nanny” is a terribly offensive word to people of West Indian descent. “Nanny” is West Indian slang for female genitalia. How could I have lived in NYC for 5 years and not known this? My babysitter is from Trinidad, and I don’t know how may times I’ve called her my nanny, the equivalent of calling her a very bad word! Maybe I’m the only one who didn’t know this, but I thought I’d put this out there for anyone as out of it as I am. Being PC is not really my concern – I’m just trying not to offend the lovely woman who cares for my kids.

There was this followup later on:

i just checked 5 slang dictionaries online, including a
jamaican one, a trinidadian one, and an english one, and found absolutely no reference to that whatsoever. my trinidadian nanny used to refer to herself and all of her childcare-giving friends as
“nannies”. now, there was some discussion in my new moms’ group as to whether the term was politically correct or should be replaced with “caregiver” or “babysitter” but generally i follow the rule of letting someone decide how they want to be referred to, so since she used “nanny”, “nanny” it was.

Actually some googling indicated that nanny could have the alternate meaning indicated in the first email.