The Dinkleberg's name is a reference to D.I.N.K., meaning Dual Income No Kids, which refers to married couples like the Dinklebergs who have large amounts of money due to not spending it on kids.
Even though Sheldon Dinkleberg doesn't seem to want (or like) children, he is willing to be involved with them as evidenced by the fact he is coach of the pee-wee soccer team named the Dinkle Ducks. He even once gave Timmy a bike and money out of kindness.
In the episode, Operation: Dinkleberg, it's revealed that Sheldon donated one of his kidneys to save Mr. Turner's life.
As 2010 "Dinkleberg..." has achieved memetic status. The meme consists of an image of Mr. Turner from "Miss Dimmsdale" blaming Dinkleberg for either something irrelevant or a world problem.
It is also revealed that Mr. Dinkleberg is allergic to dust and lobster, but however in one episode he is seen eating a lobster.