Family-Unfriendly Aesop: Carranger vs Ohranger has Kyousuke learn an important lesson, that he should always judge whether someone's good or not based on their physical appearance.
Hollywood Pudgy: Youko. A big deal is made in episode 11 about how overweight she is with everyone from the monster of the week to news reporters commending on it. When she is shown in a bikini, however, she is very slim (not helped by the fact that Natsumi is shown in a bikini besides her and looks EXACTLY THE SAME).
Not just that, but the "car" theme was already used by Kousoku Sentai Turboranger, something that was referred to even back when Carranger first came out (and Gokaiger doesn't hesitate to use for a gag). Ironically, the full title of this series was originally the preliminary title for Turboranger.
It's also similar to Blazing Saddles in that it's a comedy involving an army of thugs sent to clear out a small backwater to make way for the construction of a lucrative transport route.