3 Blind Mice - not only is it ripping the piss out of the visually impaired, its condoning violence
Jack and Jill Went up the Hill. The classic personal injury tale of woe, where theres blame theres a claim etc
Ladybird, Ladybird. I remember even as a child being distressed about this one, "Your house is on fire and your children are gone" Nice. That one makes the audience feel warm and fuzzy inside (!)
Grand Old Duke of York. Pointless. Utterly pointless, all that up and down business.
Humpty Dumpty. For contemporary tweeters a definite #fail, they couldn't put him together again could they.

Hickory Dickory Dock ok fairly innocuous... I think?
Wind The Bobbin innocuous but circular. All that winding it up and winding it back malarkey...
Twinkle Twinkle, everbody "agghhhhh", a nice gentle lullaby
Anymore? There are loads... I wonder whether other languages have similarly inappropriate nursery rhymes?!