Several episodes have decently strong horror themes (such as "The House That Jack Built" and "The Joker") to the point that they might be upsetting to younger viewers. However, those themes are strictly confined to those episodes, so viewers wishing to avoid being frightened needn't worry otherwise.
There are several episodes in which Mrs. Peel (Diana Rigg) is kidnapped and placed in perilous situations. In one episode, a deranged killer tries to saw her in half.