Visible crew/equipment: In the opening sequence, the camera's shadow on which the car roof and siren are mounted is visible as it enters the house. (00:04:00)
Visible crew/equipment: When Drebin chases the doctor out of the hospital, the doctor gets a car, while in the background, Drebin falls from the ladder. Drebin then emerges from under the car. The doctor drives off, and Drebin enters the foreground. Look in the windscreen of the car Drebin emerged from. The top of a man's head with grey hair appears at the end of the shot, thinking it's over. This is the stunt double that dropped from the ladder. (00:32:25)
Visible crew/equipment: The crew is reflected on the side of the Taurus, when it tries to stop before hitting the petrol tanker. (00:34:25)
Visible crew/equipment: When Frank Drebbin opens the car door, it is blocked by a big pile of peanut shells. You can see two large rectangular stage lights in the reflection of the car door. (00:42:15)
Visible crew/equipment: At the end of the film when the guy in the wheelchair is rolling down the stairs you can see a burst of gas (presumably from a CO2 cylinder) fire the man up. (01:18:20)
Chosen answer: "I'm Into Something Good." It's the second song listed in the music credits, and if you don't read all the credits you miss a good part of the gags in the movie.
"I'm Into Something Good" is played during the scenes where Frank is going out with Jane. The song the person is asking about is this song. Https://www.youtube.com/watch?v=wn-MlISDsNs.