Jarra says "They're very touchy about this global warming thing" to Serleena regarding taking the Earth's ozone layer, even though global warming is due to too much greenhouse gas, not ozone depletion.
When Agent K removes his digital Hamilton from the clock tower in the Grand Central Station locker, Agent J replaces it with the new Hamilton Ventura Chronograph. The next shot shows K's digital Hamilton back in the spot, replaced again by J's analog in the shots that follow.
In most of the movie, whenever Agent J and / or Agent K use the lift, they are seen being lowered down from a platform from where the lift opens to the ground of MIB headquarters level. But near the end, when both agents plus the worms use the lift to fight Serleena, the lift stops at the level of MIB headquarters, with no platform having to be used to lower the agents to the same level.
When agent Jay is trying to get off the tubes to save Laura the speaker says '30 seconds to launch' then in 10 seconds it says '15 seconds to launch' and then goes back to normal, meaning the 30 second countdown ends in 25 seconds.
During Agent J's fight against Jarra, a seam is visible in the ceiling after J recovers from being thrown against a wall. The seam is the track for the wire harness, used when J is carried to the back of the room by a flying Jarra copy a moment later.
The movie depicts the 81st Street and Central Park West subway stop as stopping for the A and C lines and depicts platforms being on both sides of the tracks. The real stop is for the B and C lines (not A) and only has platforms on one side.
Near the end when K presses the red button, you clearly see Times Square behind them. In the next shot of the car, they are seen flying through Times Square again (notice the Virgin Sign passing twice).
Code 101 Lockdown requires MIB Headquarters to be pressurized. When agent J blows a hole in the entrance, everything (hot dogs, umbrella, etc.) blows INTO the building. Most people think of pressurization as adding pressure, but negative pressurization, which creates a partial vacuum and so would suck in outside air, is also possible. It's used primarily to prevent pathogens or toxic gasses (both of which are probably present somewhere in MIB headquarters) from escaping into the general atmosphere. It's technically incorrect to refer to it simply as 'pressurization' but it's used colloquially to refer to negative pressurization by those who use it.
When J comes out of the subway, a man walks down the left side of the stairs. J then tells 2 others that the subway is closed. The men that J lets go down the stairs are wearing black suits, and are most likely MIB Agents.
If the neuralyzer is suppose to help with assisting the Men in Black in making sure that no one knows of their activities of policing extraterrestrial activity on Earth by neuralyzing witnesses, then how does Peter Graves (in a fictional role as himself) get away with knowing about Men in Black involvement with Sarleena? Did the Men in Black forget to neuralyze him? After all, it's part of their job to make sure that nobody on Earth knows about extra terrestrial activity that takes place on Earth at any point or time.
At the very beginning of the movie, Peter Graves tells the story of how Sarleena came to Earth to try & steal the light of Zaartha from the Zaarthans in 1978. However, later in July 2002; Zed mentions that that incident happened 25 years later. 25 years ago from 2002 would make it 1977. If the Zaarthans & Sarleena took place in 1978, then 25 years later would make 2003. In order for the movie to take place in 2002 after the Zaarthans and Sarleena coming to Earth fighting over the Light of Zaartha in 1978, then it would've been 24 years later, not 25. (i.e. 1978 + 25 = 2003/1977 + 25 = 2002).
When Agent K is fighting a ball-chinnian in Jack Jeebs' basement, the rubber mask material at the base of the face mask (right at the top of the scarf/sweater he is wearing) is exposed as he pulls down the scarf/collar.
In the beginning of the film when agent J and agent T first encounter Jeff's weed-looking hair sticking out of the sidewalk grate, agent T bends down to grab the "weed". In one shot, T is obviously tugging away at nothing at all. Evidently, the digital effects team accidentally forgot to add the "weed" (which was computer generated) to that shot.
When we first see Serleena's ship, we see Jay reflected on the
ship. In the reflection we see him using the communicator and talking to Zed (with one hand up to his ear) which doesn't happen until a few shots later.
In the first Men in Black film, K is shocked to hear from Frank that small galaxies and worlds can exist in our world. However, n the second film, K runs his own world in a bowling locker and knows that Earth is a world in another locker of a much larger world when he opens the door at the end of the film.
Scrad (Johnny Knoxville) disappears from the film when Jay is fighting the aliens in Jeebs' basement. He is never mentioned again, and there is no explanation or scene that shows what happened to him. Serleena later orders Scrad (who is unseen off-screen) to get Laura who is hiding in the worms' apartment. When J and K arrive at the apartment the worms tell them a dumb two headed guy took Laura. He does not appear in the big fight when most of Serleena's minions are killed.