Both Oscar and Felix mention owning a car, even though they didn't own one until, and for, one single show the next season.
As Felix is escorted off the "Password" set, he says he has two copies of the Password home version, one in his car. Felix doesn't have a car.
Though this episode--which takes place in 'current' time (I.e., the early 1970s), Oscar's "new" girlfriend Mitzi--who's this episode's "MacGuffin", was actually introduced in the second-season episode, "Speak For Yourself", which takes place in the early 1950s, where Oscar introduces Felix to Mitzi--played by the same actress, Ronda Copland, and portrayed in the exact same manner.