Revealing mistake: When the movie starts and J is about to neuralyze the people, the skyline on the background is a blatant backdrop. (00:06:10)
Continuity mistake: When they are leaving the first crime scene (the crashed UFO) in their Ford Taurus they are shown talking with headrests in the vehicle. They arrive at the headquarters for Zed's eulogy. After the eulogy they are back in the Ford Taurus and the headrests are gone. (00:07:40 - 00:09:50)
Continuity mistake: After O delivers her eulogy for Z, J and K are in the car talking. The amount of cars and the style of the streets they pass-by have no continuity whatsoever between front and side angles. (00:09:40)
Continuity mistake: During the scene where Agent J and K are driving around Midtown Manhattan, the wide shot shows them driving past the red TKTS staircase in the middle of Times Square. Then there is a shot of J inside the car a few moments later, and they pass by the red TKTS staircase again. (00:09:50)
Continuity mistake: In the car after Z's memorial, K asks J, "You lose something over there, Hondo?" As he finishes this line, J is looking at K, sitting up. In the next shot, J is looking at K with his back resting against the car seat. (00:09:50)
Continuity mistake: After Z's memorial has ended, J and K are driving. As J says "Because I was too tight", he is looking at K, doing a mime for tight with his right hand as the line ends. Next shot, he's looking straight forward, not doing the mime anymore. (00:10:15)
Continuity mistake: When K slaps Wu with the Spikey Bulba the first time, you see Wu's head turn to the right as he's hit from the over the shoulder view. But when it cuts to show Wu's face, his head is suddenly being thrown back rather than turning right. (00:12:40)
Continuity mistake: When K slaps the Chinese man with the alien crab his hair gets messy. When the shot changes it's back to brushed. (00:12:45)
Continuity mistake: Just before K says the line "I used to play a game with my dad..." at Wu's restaurant, he is looking straight forward. But as he begins saying that line, preceeding a sigh, the camera cuts to a different angle and suddenly he is looking to his right. (00:13:45)
Continuity mistake: At the Chinese restaurant, when K and J are eating, J's white napkin keeps moving around between shots, as do some of the saucers and cups on the table. (00:13:45)
Continuity mistake: When K sees the dead Chinese manager pinned to the wall, the manager's facial expression and position of his head changes between shots in a mere half second. (00:15:45)
Continuity mistake: When J is being swallowed by the fish, the floor around him swaps from very dirty, to slightly dirty, to spotless between shots. (00:16:15)
Continuity mistake: When J puts a tray in the fish's mouth, it swaps from perfect to wrinkled between the first two shots in a time-frame. For the rest of the scene, there's no continuity between the shape it has in the wide angles and in the close-ups. (00:16:20)
Continuity mistake: Trying to crush the metal tray that J wedged in its mouth, the large alien fish breaks a tooth on the tray. J then picks up a couple of bottles of mustard and squirts its nostrils full. During that shot, the shape of the broken tooth has changed slightly, and the remaining piece is larger. (00:16:25)
Continuity mistake: When J is being eaten by the fish, his trousers are clean. Right after it growls, a close-up shows his trousers covered in mustard, despite him not shooting it until several seconds later. (00:16:25)
Continuity mistake: When the huge alien fish throws J through the window of Wu's, J knocks over several rows of frogs hanging in the window as this happens. As he finishes being thrown out of the window, only one row of frogs is left. A few minutes later as K suspends J, K goes to exit Wu's and now there are suddenly two rows. (00:16:35 - 00:19:40)
Continuity mistake: When Boris shoots spikes at the door that K and J are holding, one of them gets stabbed on the upper part of the glass. When the angle changes it's stuck on the center part. (00:17:40)
Continuity mistake: After K is falling with J from the rooftop, big chunks of concrete start to fall, yet disappear in some shots. When they land, the ground is clean, yet in one of the close-ups of K a chunk magically reappears next to his head. (00:17:50)
Continuity mistake: When J and K fall off the roof holding onto a door, they land opposite to each other. A frame later, from a different angle, they're laying next to each other. (00:17:55)
Continuity mistake: After the incident at Wu's restaurant, J walks up to a crowd of people and says "Can I have everyone's attention please?" As he does, he holds up his neutralizer. Just before the cut, you see him raising his other hand and points at the device. It cuts to show the crowd, then back to J. Suddenly he is repeating this exact same motion, the footage repeated as he points to the neutralizer. (00:18:20)
Chosen answer: The name of the song is "Love is Strange," recorded by Mickey and Sylvia, and released November 1956. Pitbull sampled it in his song "Back in Time."
Chanteuse66