It was raining when the Light of Zartha made contact in the 1960's when she was meeting with K — because she was sad (for a reason).
The whole sequence with Serleena devouring a would-be rapist at the movie's start is a Black Comedy gag about models and their proclivity to bulimia—that is, eating things just for the taste, then throwing up so they'll still fit into their clothes.
If David Cross' character is intended to be the same as the first movie, it's entirely possible his obsession with aliens, the MIB, and conspiracy theories stemmed from his encounter with Edgar the Bug from that film. Getting plastered to a ceiling by alien slime would definitely be traumatizing enough to manifest as a fascination with the unknown.
Even before Zed chews out J over going through many partners and using the neuralyzer too much, it's shown that there are quite a few more MIB agents with military backgrounds than before, whether it's Agent T being an ex-marine, or the army-esque demeanor of another operative. J's antics have evidently gotten to he point that Zed is forced to take in more of the very same people previously mocked for exemplifying what he'd "come to expect from years of government training" just so MIB doesn't run short of agents.
When J neuralyses the video shop owner and tells him to move out of his mom's house, the guy picks up a shovel. Funny, maybe, but just thinking about it, was that guy planning to kill his mother?
