Trivia: The church that Dick follows the henchman into is called, Our Lady Who Never Had The Pickle. This was originally going to be the name of the hospital that Nordberg was taken to in the movie The Naked Gun.
Trivia: When Dick Steele rides the horse into the elevator, the two people already in the elevator are Loren Janes and his wife Ginger. They both appeared in the movie "True Lies" which is parodying the scene portraying the same couple in the same situation. Loren Janes even provided the stunts for this movie too.
Chosen answer: The lady in the red dress is definitely Dr. Joyce Brothers. Her presence is not a spoof of anything. Just another way to add humor to an already humorous movie.