Acting Unnatural: Rokuro tries to talk to Akemi without stuttering or looking suspicious after having an embarrassing dream about her. Needless to say, she still notices and tells Maruchi to stop waking him up before dawn for training.
Accidental Pervert: Rokuro caught sight of a near-naked Akemi, covered only by her underwear and a towel, when he hid in the girl’s locker room. To his credit, though, he didn't know what a locker room was up until then.
Bilingual Bonus: Shigeru is an English tutor, so there's obviously going to be some of this.
Chapter 9-1, Family Issues: Akemi asks for help with translating a couple of sentences into English. Shigeru does this, and then reads it back to her in Japanese. The text for him speaking Japanese is actually italicized Romaji, and in the cultural notes, these same sentences are in kanji.
Akemi calls him out for being a Lazy Bum in the chapter Family Issues.
"Let me tell you something, Rokuro-kun... You're eating here, sleeping here, and living here, for a full year, and you're not paying any kind of rent. You're basically a freeloader. My father and I are letting you stay here out of the kindness of our hearts. However, I will be damned before I let you sit around on your lazy ass doing nothing all day. One of the reasons I let you stay here in the first place was because I thought it would be nice to have a helping hand around here. Are you starting to catch on?"
He caught on.
Buttmonkey: Rokuro, who has been getting hurt in nearly every recent chapter.
Cardboard Prison: Rokuro mentions that he was tied to a tree when he was younger, as punishment. And the rope wasn’t even tight. He just forgot to untie himself.
Comically Missing the Point: In chapter 2-3, Akemi asks Rokuro if he's a good or bad wizard, meaning good or evil. He mistakes her wording, and replies with “I’m an amateur at magic... Somewhere between good and bad.” Akemi doesn’t bother to explain her question, and doesn’t ask again.
Continuity Nod: In Reversi, Rokuro flat out states that the Hakobuttori isn't the ideal way to cross dimensions because "it only comes around once a year, you don't know where it's going to appear, and you don't know where you're going to come out if you do manage to find it."
Crash into Hello: Taken to a literal extreme in the Reversi oneshot. When Akemi arrives in Mahokkai, she flies straight into Rokuro and they both fall to the ground - Hitting many a tree branch on the way down.
Curb-Stomp Battle: It's implied that the battle in the Monochrome Sector between Maruchi and Rokuro was this. After the two arrive back at the shrine, Rokuro is covered in all sorts of bruises and can barely walk. Maruchi is perfectly fine, and even entertains himself by literally poking at his student's injuries.
Expy: There has been more than one comment on the fact that Rokuro looks like Ranma Saotome. Of course, seeing as Cali first started drawing in Rumiko Takahashi's style and can't seem to grow out of it, this isn't shocking.
Similar comments have been made on Maruchi looking like a purple-haired Inuyasha. Even more so now that we've seen what he looks like as a full-fledged adult.
Facepalm: A marvelous, apparently audible one is given by Maruchi towards the end of 14-1 after this exchange:
Fish out of Water: Rokuro, and Maruchi. Two magic users, one being a mostly-hormone-driven wizard boy who can’t fly without assistance from a cleaning object, the other a racist child with purple hair and animal appendages, both never having made any contact with humans before. They’re way out of the water.
Lethal Chef: If Akemi and Emiri's comments are to be believed, Meiko is a serious case.
Living Shadows: They're under the control of a kage-nushi, or 'shadow general', who invades Rie's home in the tenth arc. The personality of the shadow general doesn't exactly match up with his power, though...
Loads and Loads of Characters: Nineteen main characters in all. And that doesn't even cover all of the ones that are going to appear in season one.
Magibabble: Maruchi delivers this every so often, usually to help Akemi understand what's going on.
Magic Skirt: Akemi’s uniform skirt doesn’t flap up at all when Rokuro flies her home, as worried about it as she is.
The Mind Is a Plaything of the Body: Maruchi acts much more like a kid when taking the form of one, even though he's actually an adult. A theory given is that he's spent so much time as a kid that his mind has become somewhat wired like one.
Mind Rape: Shichi is perfectly capable of using his abilities as a shadow general to mind rape innocents. His first Earthly victim? Rie.
Missing Mom: Akemi's mother has barely even gotten a mention yet.
As of chapter 23 (Thick and Thin), she has. Her name is Hazuki. She's also dead. In that same chapter, Rokuro reveals that he has also been without a mother since he was six.
Mistaken Identity: The substitute teacher Hizen Umiyoshi mistook Akemi for her mother Hazuki. He had to be corrected by another student.
Never Say "Die": Shigeru always refers to Hazuki's death as her being "gone". The rest of the family does the same, out of respect.
No Name Given: In the (revised) chapter one, Rokuro makes it clear that he doesn't have a last name to give.
"I'm Rokuro, a Type One wizard. No last name applicable."
Noodle Incident: What exactly did Rokuro do that humored his boss enough to hire him? And how did he almost get himself eaten by a giant chameleon?
No Punctuation Is Funnier: What the hell is going on here why is this happening why is Akemi kissing me when she has a boyfriend holy crap Maruchi and her dad are right over there watching I'm going to die soon I know it why me wait why am I outside again
Not What It Looks Like: Until Akemi explained it to him, Shigeru thought his daughter was being... impure while he was on his trip; of course, his first sight upon entering his home was Rokuro in his boxers...
Oh Crap: Rokuro’s exact reaction upon seeing his teacher in the human world. Also his reaction whenever he sees Shigeru.
Sleep Mode Size: Maruchi sleeps in his kitten form to conserve energy. Once he regains his original self, he spends his nights in his true form.
Spell My Name with an S: Rokuro's name is written as 碌労, meaning something like "worthy effort", whereas the usual spelling means "sixth son" (六郎). It must be common to misspell his name, because Akemi once wrote it as the latter and Rokuro instantly knew she meant him.
Hakobuttori (ハコブットリ) is a portmanteau as well. Uttorisuru / uttoritosuru means "to be fascinated' (In a world of one's own), or "to be transported" (In terms of your mind, i.e., daydreaming). Hakobu means "to carry, transport, or move".
The lettuce joke in chapter 2-1. The pun uses Japanese, English, and Latin.
Majikyou (マジ教) is made up of the first two katakana in majikku (magic) and the kanji for "teach". A majikyou is a magic teacher.
Hell, even the high school's name is a pun - Okashii (可笑しい) means "strange". However, the kanji used in Okashii High School are 陸 and 椎. The first means "land, shore"; the second is a type of tree.
Rokuro's "serious chant" VS "thinking chant" in chapter 7-3, Conscience.