Synonyms for Peculiarity (same or very similar meaning)
WordNet sense 1 (an odd or unusual characteristic):
distinctive feature, distinguishing characteristicWordNet sense 2 (a distinguishing trait):
distinctiveness, speciality, specialty, specialnessWordNet sense 3 (something unusual -- perhaps worthy of collecting):
curio, curiosity, oddity, oddment, rarityFrom the ODE community, based on WordNetadd/edit