When Duplica says Ditto is one of a kind, and no other Pokémon can transform, that's incorrect. Mew can as well. This is most likely because she either doesn't know about Mew, or doesn't believe he's real. Interestingly, it is rumored that Ditto is the failed experiment of cloning Mew, which would explain why they can both transform.
Duplica is based on the 'Copycat' character from the first generation games.
This is the first time that Ash and his friends mock Team Rocket's motto completely.
Duplica and Imite are just shortened versions of duplicate and imitate which are synonyms of what ditto does.
American Title: "Ditto's Mysterious Mansion".