When M is in High T's office after the club scene, there is a close up of her hand fumbling around in her pocket. Within a split second, going to a wide shot, her hands are together in front of her.
When Agent H and M land in the desert, Agent M's sunglasses are on the sand under her feet. In subsequent scenes, they are no longer on the sand, and there is no indication that she moved them.
Upon arrival at MIB's London branch, M is given a watch by High T. When she opens the box, the watch top is at the left, but after reading the card, the watch top has switched to the right.
After H and M land in the Merzouga desert after H hits the "red button" acceleration on the hover bike, they somehow manage to start a campfire, despite the area being devoid of vegetation.
Whilst in London an explosion throws a manhole cover into the air. The manhole cover is round. In the UK all manhole covers are square/rectangular in shape. This is a US manhole cover.
When Agents M and H first arrive to meet Vungus they can be seen driving along the right hand side of the road with cars driving along side them giving the impression that they are driving on a one way street. However, if you look closely you can see that there is a keep left sign, a painted 20 zone sign and a painted bicycle in the cycle lane which are all facing in the opposition direction which would be in the direction of traffic flow. This indicates that the road was used as a one way street purely for the intention of filming. You can also see a sign for the central criminal court which is also facing in the same direction as the other traffic signs.
M tells H: "Physical attraction is nothing more than chemical reactions in your brain", but her mouth doesn't move.
Just two agents (H and High T) to investigate the portal breach at the Eiffel Tower makes no sense.
Molly hacks into the Hubble Telescope to locate the Brooklyn MIB containment site without any repercussions.
Portal 2 at the Eiffel Tower is closed, and the door High T and H encounter should have been blown off.
As the train Molly boards can be used by MIB and their alien allies only, then it makes no sense for it to "transform" from an MTA train into a "super train", especially as it does not convert back into an MTA train after it arrives in London.
The couple Agent H and High T encounter at the Eiffel Tower are obliviously there after the Tower has been closed to tourists.
Agent High T. mispronounces Centaurus as "Centoo'rus". It is pronounced "Cen-TO-res" or "Centaw'res".
The being in the shape of a pair of men's shoes Molly encounters on the train make no sense as an alien.
When taking off in the car from London to Paris, the internal shot suggests they took off from an airport, as there is a runway in the background.
When M travels to London from New York, which is west of the UK, you see the "subway" heading towards Tower Bridge. However it is approaching from the east.
This film states the first alien migration to Earth occurred in 1889; in Men in Black (1997), it is established that first contact was made on March 2, 1961. Contact is different from migration, with one establishing the existence of aliens, and the second allowing them to immigrate to the planet.
There is nothing keeping the 3-headed snake from escaping the cage as its door swings both ways.
Molly is placed on a probationary period. If she fails to make MIB, she will have no way of retrieve her identity (fingerprints, birth certificate, Social Security number, etc.), which has been erased.
Molly is not vetted; apparently, her determination to find MIB are all the "qualifications" she needs to join on a probationary period.
It's never explained how and where H got the powerboat or how and where he and M obtained civilian clothes.
H has M neuralyze the Marrakesh street vendors and shoppers after he crashes his bike, which hundreds of more people watch him "ride" moments later without being neuralyzed.
Not only does MIB not have security at the containment area Molly enters, anyone could have seen the pigeons "evaporate" into the fence. Ironically, MIB does have security and vertical light stands placed at later containment areas.
When M stumbles upon the idea that MIB has a mole, C gets ready to neuralyze her (convinced she's the mole). She and H put their sunglasses on while pleading their case to High T, who doesn't have his sunglasses on.
The MIB agents don't neuralyze Molly because her parents tell them that she is in her bedroom sleeping. All the agents had to do was look up and see that Molly's bedroom lights are on.
When Agent O orders one of her goons to neuralyze Molly, Molly turns her head away instead of covering her face.