This is a bit of a perplexing question. "Special" in what context? Special from other characters in literature? Special from the influencing story behind the grisly tale of "The Veldt"? Special in context with each other? Special in context of the story or society? The definition of "special" is:
special: distinguished, set apart from, or excelling others of its kind (American Heritage Dictionary)
We'll try examining this question in context of the story itself: What distinguishes these characters in context of the story? First, the mother is distinguishable for her ambiguous feelings. On one hand, the nursery terrifies her:
"I'm afraid." She came to him and put her body against him and cried steadily. "Did you see? Did you feel? It's too real."
On the other hand, she is overwhelmed by her children's emotionalism and profoundly manipulated by them (i.e., manipulation: to intentionally influence deviously (AHD)):
"George," said Lydia Hadley, "turn on the nursery, just for a few moments. You can't be so abrupt. ... You can't be so cruel ..."
George is intelligent and deeply caring. His actions, whatever the unseen consequences might turn out to be, are motivated by compassion and care; he is not demanding, dictatorial, heartless--nor is he comfortable with being stern where needed:
"Oh, George," said the wife, "it can't hurt."
"All right—all right, if they'll just shut up. One minute, mind you, and then off forever."
Peter and Wendy are selfish and cruel and unfeeling. Psychologist David McClean asserts that is the fault of over-pampering by their parents--however, it would have been an unintentional result of kindness, love and care. There is no better proof of the way in which Wendy and Peter are special than to redirect attention to the end of the story:
Mr. and Mrs. Hadley screamed.
And suddenly they realized why those other screams had sounded familiar. ...
"A cup of tea?" asked Wendy in the silence.
One can only but wonder what happens to Mr. McClean ....