In a Call-Back to the original series, Deslar's Trap Door for annoying generals. Plus, the way he opened it implies the whole room is filled with trap doors, with Deslar remembering the position of every single one and the related command.
To make this funnier... The trap door's victim has a name and background on the official site! He's Dotem Gelhen, minister of food resources and chief of the food production bureau.
And for the punchline... We have how those present reacted to it:
"Long live our leader!"
During the mutiny, the doctor and nurse Harada had an Offscreen Moment of Awesome taking down the two mutineers keeping Okita confined to his room. When we see Okita free, we have a cut to his room, with the small doctor dancing with his sake bottle in one hand and the gun of one of the tied-up mutineers and Harada threatening the other by aiming the stock of his own gun at him while wearing his helmet, and the two poor sods are still wondering what the hell has happened.
In episode 4, Kodai and Yuki are in a mission with Makoto, with the latter convinced something romantic is going to happen. After Yuki catches him staring at her, Kodai makes a question:
Tokugawa jokingly trying to get Shima with his granddaughter. His toddler granddaughter.
Kodai and Shima nearly beat each other up. Their punishment? Cleaning the whole ship, starting with the barrel of the Wave Motion Gun.
Kodai telling Yuki bluntly that he doesn't think she'd make a good pilot like Akira, which caused her to face-fault. Funny if you realize that in the live-action movie, she's a fighter squad leader.
This was revisited in a later episode when she asked him to let her pilot a fighter they were running a recon mission after they determined that there were no immediate threats. When he refused, the two resorted to pulling ranks on each other...all of which was being broadcast straight into the Yamato's bridge. Naturally, everyone assumed they were flirting.
Yoshikazu: 003, this is the Yamato. Sorry to interrupt, but we can hear everything you say.
Kodai & Yuki: O_O
Pretty much every single facial expression of Goer.
Especially his Luminescent Blush when Dessler got fed up with his hamminess during a radio communication and told him to just do his best.
Goer's reaction to Zoellik's hamminess - even more funny since Goer is a huge ham himself!
In episode 21, Yuki dealing with the fact the Gamilans mistook her for Yurisha, and thus treat her like royalty and expect her to dress in the very immodest style of Iskandar. She then starts acting the part.
From the same episode: Kodai is about to take off with the Seagull when Yurisha, who is on the co-pilot seat, asks him if he wants to save Yuki, because she wants too. He looks at her for a moment, returns completing the pre-take off checks, and then has a startled Double Take when he finally registers her presence.
He tries to get her down for a while, and in the end resorts to answer her question: he'd do it if he knew where Yuki was. Yurisha replies by pointing out she's on the planet he's supposed to scout. They immediately take off.
While they're travelling, Kodai asks Yurisha how she knows Yuki is on that world.