Percy Takes the Plunge - S2-E11
Character mistake: Henry says "This shed is for the Fat Controller's Engines!" to Bill and Ben, but they ARE the Fat Controller's engines.
Suggested correction: Bill and Ben were not owned by the Fat Controller.
Percy Takes the Plunge - S2-E11
Deliberate mistake: When Percy is being loaded onto the flatbed, Diesel appears, but he is not introduced until "Pop Goes the Diesel" (episode after this). This is likely because "Pop Goes the Diesel" was produced before this episode.
Suggested correction: There is nothing in the show suggesting that the episodes are shown in chronological order.