Since Ted is meant to be telling his children the story of how he met their mother over the course of one long conversation, his son and daughter are shown wearing the same clothes throughout almost every episode.
The one exception is the pilot, where the daughter is wearing a gray cardigan, skirt, and tights, and the son is wearing a dark polo shirt and jeans.
For the rest of the series, Ted's daughter wears a pink cardigan, shirt, and pants, and the son wears a shirt, hoodie, and jeans.
The background behind the children is also a little more cluttered after the pilot episode.