Continuity mistake: When M travels by train from New York to London, we see it crossing the Atlantic west to east. We then see it traveling east to west under the River Thames at Tower Bridge as it comes to a stop in London.
Continuity mistake: In the first movie it is stated that the program was started In the 60's, but in this one it is stated that Gustave Eiffel was an MIB agent.
Continuity mistake: When young M finds the creature, the rugby shaped plush toy behind it is either next to the edge of the table as seen in the wide angle, or away from the edge in the angle shot from behind.
Continuity mistake: When young M is woken up by the doorbell her right hand is either away or on top of the book, depending on the shot.
Continuity mistake: When M's dad shouts and scares her mom, her arm is either raised or lowered depending on the shot. (00:04:40)
Plot hole: When young M has the alien in her room, why don't the agents remove the alien from her room before erasing her parents' memory? If M didn't get rid of the alien out the window, they would just have to come back. (00:01:00 - 00:04:00)