Continuity mistake: When agent H is being chased by the MIB agents through the market streets of Marrakesh, he runs past the same extra twice in two separate streets: a young guy with a goatee, wearing a brown robe with red collar and a backpack.(01:02:00)
Plot hole: Molly disturbs some birds at the hologram causing them to fly off. First off, the birds don't react realistically at all in how or where they fly to. Then secondly the birds fly directly at the fence part of the hologram and go through it. This is a visible construct to the eyes as a fence, and thus the birds would see this as an object in their way as well. Even if the birds saw what was there before and saw the hologram appear, they would not posses the knowledge or intelligence to know it was something they could just fly through and would go over it.(00:10:38)
Trivia: To date the only "Men in Black" film not directed by Barry Sonnenfeld, and the only "Men in Black" movie not to feature Tommy Lee Jones and Will Smith. (Although a painting of Jones and Smith is visible in the film).