The PatRangers film a movie somewhere right next to Oomori-zaka.
The movie studio is Tokai, a parody of Toei. The kai portion is the same kanji they use in Kaitou.
Pitch Cock is a play on the word peacock + Hitchcock. His spell Peacockazam (クジャリンパ kujarinpa) is the Japanese word for peacock (kujaku) plus a magic word-type suffix (rinpa).
When their sexes are flipped, the PatRangers' names are adapted to match (Keiichirou>Keiko, Sakuya>Sakimi), except for Tsukasa, who already has a gender neutral/boyish name, so they keep hers the same.