Plot hole: Spoiler. Agent M points out as highly suspicious that the twin assassins knew the location of Vungus, and High T backs her up on this, saying that only a handful of MIB officers could have leaked that information. High T also established that those aliens were part of the Hive collective. It turned out that they were not part of the Hive, and the Hive connection was made-up entirely by the villain himself...which is the Hive! What he did was absurdly counterproductive to his cause: nothing except the report he himself made up connected the Hive at all with the case.
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.
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)
Plot hole: Spoiler: It appears entirely impossible that the Hive plan (which apparently involved just...waiting around indefinitely for a specific weapon to turn out, if you listen to H's summarization of it, which T agrees upon) could ever work, in particular for years as depicted: H 's mental conditioning literally does not go past one sentence he memorized, and breaks down if asked for any detail. He could never have filled a mission report or be engaged in conversation about the subject. And High T has Hive DNA: we have to believe that MIB does not conduct as much as an annual physical on its members - and that considered that other high officials were suspicious of him to begin with. (01:36:00)