Theo is in the hospital because of an accident he caused at his high school chemistry lab (Chapter 20).
In trying to decipher the clues he has been given in the Westing Game, Theo discovers that if he arranges the words in a certain way, the clues present a formula for an explosive (Chapter 17). He experiments with the formula using chemical fertilizers, but makes "a slight miscalculation", causing the lab to blow up. Fortunately, no one else is around at the time; Theo himself is injured and ends up in the hospital emergency room. Theo's injuries are minor, and after removing glass shards from his shoulder and patching him up, the doctor releases him with "a warning about careless chemistry" (Chapter 20).