In general, all the shout outs to anime are pretty funny. Which is justified as the main character is an otaku and trying to spread otaku culture.
Episode 1: When Shinichi meets Miusel, he is first reaction is to scream, at the top of his lungs, "Holy crap, a maid". Then grades her with a really fanatic look in his eyes. When he is told he is her master, he just says, "Holy cow, I'm a master!".
When he meets Minori, he just calmly guesses what her cup size is. She corrects him when he gets it wrong.
After Shinichi is told of his job, Shinichi is scared of the pressure and tries to leave. Matoba just asks him how to leave.
Shinichi gets an e-mail from his mother, which gives him three choices for the future. 1. Go back to school. 2. Get a job. 3.Get disowned.
Petrarca and Shinichi are reading an expy of Attack on Titan, and she tells him not to stop reading as "It's almost at a good part," after it says that the two kids were saved from the Titan. They turn the page, and any fan of the original work will know exactly why the "Supreme Ruler" has that look on her face.
Shinichi and Minori walk into classes to find an argument between the elf and dwarf students. He fears that the racism of the world is acting up. It turns out they were just arguing about the merits of dating sims versus figurines. When another group of dwarves break up the fight, calling it 'childish', Shinichi at first thinks that his class still has some sensible people. Then, the group introduces themselves as the 'Little Dwarf Girl Guardians'. Eventually, Minori brings a stop to the argument by firing her gun at the ceiling.
Minori helping Gallius understand otaku culture by lending him BL manga.
Gallius: Do not worry. I do not "bat for both sides".
In the dub, he refers to the experience as having been "enlightened."
Elbia seems to be plotting something very evil towards Shinichi throughout the episode... turns out she was just in heat, though.
When Miusel sees Elbia on top of Shinichi, she just calmly walks away. Or her reacting uncomfortably to Minori's suggestion that Elbia likes Shinichi.
Minori is determined to get Shinichi to teach BL and he constantly shoots her down. Then it is revealed the government is forcing Shinichi to teach it.
When Petrarca summon's Shinichi and Minori to her throneroom for an audience, she beings acting all Tsundere again, attempting to get it across to Shinichi that she knows about the workings of the trope (and possibly that she recognizes herself as one). However, at least in the dub, she refers to it as "that Tundra-thingie," prompting Shinichi to correct her that they're two different things.
Petrarca: The otaku culture truly is profound, isn't it?
Shinichi admitting due to Minori firing her gun so often, that the sound of gunfire doesn't bother him anymore.
Shinichi, Minori, Elbia and Miusel receive otaku goods from Japan. Minori gets a soccer ball from InazumaTwelve which Elbia instantly plays with. Minori goes into such a rage that she has to be held back by a few soldiers.
Shinichi, hoping to improve relations between elves and dwarves, suggests a soccer game. Both sides study with different series. Minori personally gives the elves uniforms based on InazumaTwelve and fangirling over them during the game.
The game is freaking hilarious. It starts with the dwarves painfully dominating the first half, due to their superior physical abilities. It got so bad, the dwarves let the elves use magic in the second half, in order to make things more even. Things escalate, until both sides forget about the match and just start fighting one another by lobbing magic and boulders. By the end, every player is curled up in the middle of a crater.
The rice scene. Shinichi convinces the Erdantians that, when somebody has rice on their face, the Japanese custom is to pick it off and eat it. He does so for Petrarca, which causes him to fanboy and appear with angel wings and cherubs. Then Garius noticed that Shinichi also has rice left on his face, so he picks it off and eats it, calling it an interesting custom. Minori is seen in the background, ecstatic.