DDs 1 and 2 met children like that in the Appalachia region of the US on a church aid trip. 'Mountain Dew Mouth' is tooth decay caused by lifelong drinking of Mountain Dew, starting with the baby bottle in many cases.
As for children not knowing nursery rhymes - not so much a problem if language development is otherwise on track imo. Many children have nannies who don't know English nursery rhymes. If they've never been read to in English and English is their first language then I think that's more of an issue. Singing in another language or learning rhymes in another language is fine. I knew children who spoke more Spanish than English in the US as their nannies had all been Spanish speakers. Their English needed a lot of fine tuning when they got to school and their reading was a bit behind their classmates - on a par with bi-lingual children, which they were, with Spanish dominating.
I know many children who have had a string of nannies and not much contact with parents; very insecure children, sad for them.
MarvintheMartian - I know of a 2 yo child of very well off parents, both older, who can barely speak, possibly because his parents and apparently his daily CM never talk to him. My sister knows the mum and watched their interaction (complete lack of I should say) and was very surprised. When she was trying to get to the bottom of it with her, she asked the mum if she ever read to the DS. The reply gobsmacked her - 'I didn't know they could read'. The parents are in fairyland. Child spends all day in CMs and the CM has now been encouraged to talk a lot with him in an effort to undo the damage...
Nappies - again SNs can result in various problems in potty training. Not in itself an indication of poor parenting.