Not sure about 3, but in 2 Scott Baio's character Stan Bobbins is the brother of Peter MacNicol's character from the original.
http://www.freewebs.com/demonictoys/
I haven't actually seen any past part 2, but from what I can glean, apparently the Super Baby Team from part 2 (probably with alternate babies by now, but maybe the same powers) travels the world, solving crimes.
On a side note, Leo, Gerry and Myles Fitzgerald, the triplets who played Sly and Whit in the original, have become quite the hockey phenoms in Canada.
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We never really grow up, we only learn how to act in public.
What that other user didn't mention is that some of the actors from the 2nd movie reprise their roles in this one.
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