Continuity mistake: In the beginning of the movie when the guy with the long beard starts to talk you see Frank standing disguised by the table. When it cuts Frank is moving towards the table. (00:01:25)
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)
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)
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: When Nordberg stumbles out the door on the ship and about to fall over the rail you see him going out the cabin crouching with his head first. When it cuts to a wider shot from outside you see him walking calmly against the rail before falling over. (00:07:00)
Continuity mistake: When Nordberg is in the hospital for the first time, Frank comes. Before he walks in, Nordberg's hand is on his side, and when Frank finally walks in, his hand is on his stomach. (00:10:05)
Continuity mistake: When Frank sits down on Nordberg's hospital bed and the bed breaks up you see three tubes on Nordberg's chest. When it cuts an extra tube appears on Nordberg's shoulders. (00:10:05)
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)
Continuity mistake: When Frank has his speech and says "No matter how silly the idea of having a queen..." you see the mayor turning her head to the right. When it cuts she is looking to her left with a rather shocked face. (00:13:55)
Continuity mistake: When Ludwig picks up his gold box you see him holding the box in different ways between the shots. (00:20:10)
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)
Continuity mistake: In Ludwig's office, the position of the tissue papers changes between shots. (00:21:20)
Factual error: Frank hits some garbage cans with his car and the air bags deploy. He gets out of the car and another air bag deploys underneath the steering column and pushes up on the automatic gear shifter, which presumably makes the car start rolling. If the engine is off, a car will roll with the shifter in any position except park. Therefore, the shifter had to be in park when he got out, so pushing up on the shifter would not make it roll. (00:25:20)
Continuity mistake: In Ludwig's office, when Papshmir is with him, you see a wide shot of Ludwig's desk and you can see a small remote control. When it cuts to Ludwig picking up the remote, another item appears beside the remote. (00:27:55 - 00:28:40)
Continuity mistake: In the scene where Frank is in the driving school car chasing the doctor, right after Frank says, "I know a shortcut. Turn left here", we see two brief shots of the doctor's car, one from the inside of the car and the other from the outside as he is turning around a corner. In both shots the rear window is shattered. However, it is only four shots later that Frank shoots at the doctor's car, shattering the then intact rear window. (00:31:45)
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 Drebbin is riding in the back seat of the "driver's ed." car, the gear shift stays in the same position even when the car is reversing. (00:32:45)
Factual error: In the scene where Frank is in the car, and the Doctor shoots at them, the windshield breaks right out and pieces fly all over Stephanie (the driver). This could only happen with a window made of something like plate glass. All windshields since before the 1940's have been made of a glass that will not break as a plate glass window does, so the bullet should go through the glass and just leave a little hole with cracks all around it. (00:33:15)
Continuity mistake: After Frank commandeers the driving instructor's car for a chase, the woman learning to drive is faced with an oncoming truck. In one shot, the instructor has glass all over him, but in the next shot of him, the glass is all gone. (00:33:30)
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.