Peter is a boy who refuses to bow to parental authority, which is a long way of saying that he's just like Peter Pan. Wendy is the girl that follows Peter, just like in Peter Pan. David McClean is the guy called in to clean up the family. Bradbury wants us to understand these characters quickly since this is a pretty short short story (try to say that five times fast—and you'll probably take more time than the story). So he gives them meaningful, culturally significant names.
This isn't just a characterization tool. Family life is a big honking theme. In any case, we get to know the characters through the way they act as a family. And especially through the ways that they fail to act like a family. George can't control his kids and Peter makes casual threats to his dad. That's a big problem and it tells you that while George is ineffectual as a papa, his son is a class-A maniac. This tension pops up a lot, like when Peter tells Wendy to go check out the nursery and George tells her not to (106-108). Guess whom she obeys? Like all good little girls, she does what her evil twin brother tells her to do.
The kids gorge themselves on hot dogs and ice cream at the carnival. So we know that the kids are eating junky carnival food rather than dinner with the family, which tells us that family isn't so important to them. And that they do whatever they want.
But it's also important to see how the food is made, which brings us back to technology. The kids may be spoiled junk-food eaters, but their parents are spoiled, too. For crying out loud, they don't know how to cook without an automatic kitchen.