Akane & Gino's digital avatars in Episode 4. Akane's is a Super-Deformed version of herself, while Gino's is... a giant nickel. As in the American coin. That has "Liverty" spelled on it.
In Episode 6, Akane goes to Kagari to try to pry a bit more into Kogami's past as an Inspector. When Kagari wonders at her reasons for doing so he asks her if she just might be in love with him. Her response is the only time she laughs in the series.
It seemed like it was only the second time she had even seen alcohol, saying, "... You mean it's not for breathing fire?" The first time she'd seen it, Masaoka had used it to set off a building's sprinkler system, to disrupt holograms that the episode's perpetrator was using to confuse the team and cover his escape.
Akane doesn't want to talk about the Specimen murders because Kunizuka is eating and Akane is worried about making her lose her appetite. Kunizuka doesn't see the problem and goes on quietly eating her noodles.
Episode 7 sees Akane Eating the Eye Candy. She shrugs it off rather nonchalantly when Kogami asks if there's anything on his face.
Episode 8: While the specimen case is gruesome and horrifying, the tale of a corrupt politician that claimed he had no recollection of illegally altering his psycho pass being found with his brain removed and his hippocampus (the part of the brain responsible for memory) stuck up his backside is pretty funny.
In Episode 10, Kogami realizes that Yuki is the key to finding what they need to escape and tells her to Take Off Your Clothes. Yuki is indignant, but complies. She throws her bra at him... and it lands on his head. The best part is when he doesn't even react.
While mostly a dark episode, episode 11 has a rare moment of funny, when Masaoka stops an injured Kogami from running off...courtesy of a wicked headbutt.
In Episode 13, Kogami returns to work after being in the hospital due to events of Episode 11. When Yayoi asks about his injuries, Kogami says that he threatened to set fire to his hospital room if they kept him any longer. Kagari's response? "That's the Ko-chan we know and love." The kicker? Kogami says he was just kidding.
Episode 16: In addition to being an Awesome Moment for Akane, there is something beautifully hilarious seeing Makishima, who has just finished kicking Kogami's ass and preparing to kill him in the same manner as he killed Yuki, get taken down via Akane hitting him with one of his own helmets.
In a meta-example, Gen Urobuchi tried to avert what happened with Aldnoah.Zero, where he was repeatedly Misblamed for the show's direction when in reality his involvement was rather minor. An alleged livestream on Nico Nico Douga on Sept. 22, 2014 had Urobuchi stating "Don't blame me if people die in Psycho-Pass 2, that's Ubukata's doing!"
Mika thinks that Akane's Hue is messed up when she, Ginoza and Sakuya check the latter's home for signs of intrusion in the 4th episode.
Mika: Inspector, there's still plenty of time to save your hue with the right therapy.
Akane: Are you insinuating that I vandalized my own home, Inspector?
The mysterious "W.C.?" written on the wall is being investigated. Ginoza of all people is the first to suggest "Water closet", aka the bathroom. As Mika puts it, "If you have to go, then go!" It gets better when Mika and Yayoi's guesses get even more off-track with "World Cup" and "wild caught" (as in salmon).
In episode 7, Mika comes into the office late at night looking for Yayoi's help on the case. The look on her face when she realizes Hinakawa is the only one there is priceless. Then she grumbles, "I suppose you'll do." So where was Yayoi then? Answer: in bed with Shion.
After Arata and Kei report back to Mika on the investigation of the Hyper Transport corporation's drone crash, it turns out that they've been stepping on a lot of people's toes, with five agencies & corporate offices sending complaint letters to Mika's desk. She's so irritated with them that she grabs what looks like a Pez dispenser and starts shooting candy tablets into her mouth as if it was a spray bottle! Bonus points for the "head" of the dispenser being one of the kawaii drone holograms the Bureau normally uses.
The Info Dump on the Subprime Crisis (a reference to the 2008 Financial Crisis) has the Kawaisa mascots with the characters' face on it. While it's a very informative presentation, it's also very hilarious.
Mika meeting Ginoza again in the second episode. She seems to really have it out for Frederica for, as she says, "poaching my most capable detectives." Ginoza then points out that she just complimented him... which she hilariously tries to deny.
After Tenma explains he's nihilistic about martial arts clearing Hues, Yakushiji, one of the candidates running for governor, gives him a slap and a head butt telling him not to give up and do his best so he won't stay as a latent criminal forever. Then, he gives him a hug before he leaves.
Mika getting even further exasperated over even more complaint letters about Arata and Kei landing on her desk, this time from the election campaigns of both gubernatorial candidates. As she puts it to both of them, "Are you trying to get me fired?!"
Arata being temporarily rendered as chubby in the car after the group ate. The style that Arata is animated in is hilariously off-putting, making him look more like a Moe character from a kids' show, especially when he has a dopey smile on his face.
After discussing the case, Arata presents three questions on the table. In order, how did they send attackers without detection, what's in it for Enomiya, and how was the ramen so delicious. Irie and Kei are amused. Todoroki...not so much.
Once again, Mika gets furious at Arata and Kei for arresting a state guest without her authorization. She throws her Kawaisa mascot at the wall which bounces back before she catches it. Then, she squashes it with her bare heads and lits it on fire.
When Shion does a Compatibility and Aptitude Examination on the Divison 1 members for their undercover investigation, it turns out Kei and Mao are compatible, much to Irie's dismay who ends up being compatible with Hinakawa of all people. As for Arata, he's incompatible with everybody in the division, having a D- score with everyone... except for Mika who he gets a D+ with.
There's some Black Comedy when Kei got tasered in episodes 6 and 7. In episode 6, he and Mao are both knocked down when one Heaven's Leap guard taser them. Then, he gets tasered again after he and Maiko are cornered. And then, he gets tasered again after beating the guards. And the one who keeps tasering him is no other than Ginoza himself.
After the Heaven's Leap case is closed, Mika orders Sugo and Ginoza to tell her "threatening" message to Frederica. Of course, Sugo rejects it in a deadpan way. Clearly, he and Ginoza are having fun teasing their former boss.
Towards the end of the movie, Mika is shocked to see Homura as the new bureau chief. It becomes more hilarious when Homura informs her that she will have an assistant: Akane, her former partner who is now a Statutory Enforcer. Mika's reaction to it is basically priceless.
Zack Bolton mentions in commentaries that he made the voice actors watch the scenes while they do their lines on purpose to gauge their reactions, especially if the Dominators are involved. Depending on your view, it's either Crosses the Line Twice or Played for Laughs.