The scene about J's dad at Wu's restaurant may have been Played for Laughs or something else. It becomes harsher when we find out the identity of J's father and his fate. It also manages to kind of explain K's role as a father figure to J.
"Have you ever flashy thing'd me before?" in the first movie is now far more poignant, almost to the point of being Fridge Horror.
In the first two films, the majority of the aliens were done via CG with some practical tossed in. In the third film during the 1969 scenes, most of the aliens are done via practical makeup/animatronic effects via Rick Baker, to give them a more "retro" feel similar to how they would have looked during that era.
In the first film, Jay mentions having suspected that his third grade teacher was an alien from Venus, to which Kay confirms was from Jupiter, or rather, one of its moons. How Kay could possibly know about Jay's childhood becomes more understandable after the third film, in which Kay sees himself as a father figure after accidentally getting Jay's father killed in 1969. Plus, it shows that Kay always thought Jay had the potential to become an MIB agent.
While K's increased stoicism in this film can be seen as Flanderization, especially in comparison to the first film, a lot of events between the two films affected his persona. In the first film, there was the hope of retirement in the form of being neuralized and reunited with his old girlfriend/wife. (He would be relieved in not knowing all those 100+ memories he didn't want.) By the second film, he is emotionally detached from civilian life to the point in which his wife left him. He is resigned to the fact that he will always be a MIB agent until he dies whether he likes it or not. Also, by the end of the second film, he had to relive the death of Lauranna and say goodbye to (presumably) his daughter. No wonder he doesn't crack a smile anymore.
Boris not only killed his "girlfriend" and a bunch of guards during his escape, but probably killed a lot of other prisoners, as many walls and airtight doors as he blasted through. Fortunately, all of this is mitigated by the reset after Boris is properly defeated.
It's stated that J's memory wasn't changed by Boris's time changing because he was present in the event. We later discover that J was present AS A CHILD, and son of the colonel overseeing Apollo launching. Which means that in the Boris Wins timeline, the young child probably witnessed K's death, and likely his father's death as well (and maybe seen Boris' real form), before getting mind-wiped by the MIB clean-up crew. And the mind-wipe as a child would explain why J wouldn't remember the event in ANY alternative timelines the time travel change created, but would still be aware of it.