Continuity mistake: When Frank is fishing the pen out of the fish tank and the fish gets attached to his nose, there is visible blood. When the camera cuts back to Frank, the blood is gone. (00:20:35)
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)
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)
Continuity mistake: In Ludwig's office, the position of the tissue papers changes between shots. (00:21:20)
Revealing mistake: When the window slams on Nordberg's hand it is that the window stops right above his hand. When he pulls his hand out the window doesn't go all the way down and a wooden cube is visible on the edge of the window stopping it from closing. (00:06:50)
Continuity mistake: In the beginning of the movie, during the big fight, Frank grabs Mikhail Gorbachev and smashes his head through the wall. The guy stays there but at the end of the fight, when Frank is about to jump out of the window, it shows him again. The hole now is bigger and not only consumes his head but all the way to his waist. (00:02:15)
Continuity mistake: When the "I LUV YOU" picture is viewed in Nordberg's hospital room, the photo has a vertical/portrait orientation. When Frank shows the picture to Jane, the photo has a horizontal/landscape orientation. (00:12:50 - 00:38:25)
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)
Continuity mistake: When Ludwig picks up his gold box you see him holding the box in different ways between the shots. (00:20:10)
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.