In Episode 2, Mai cheats at the stairs-climbing game by recalling a "spell of resurrection". It's later revealed this is a password for Dragon Quest, and what she enters is incorrect. She was making an obscure video game reference that very few people would get (never mind her friends), and she's been getting it wrong all this time. Good thing she wasn't with another hardcore fan.
Obscure in the West. In Japan, Dragon Quest is more popular than most religions.
"First comes rock, then comes paper / You can't throw all of them..." Mai tries to in Episode 5 and scores a Critical Hit. Then again, it might be because most people don't have a solid wooden statue handy.
An interesting detail when you pay attention is that, while segments featuring the trio of Mio, Yukko, and Mai are frequently sprinkled with Mundane Made Awesome, the segments with the mad scientist, wind-up robot girl, and talking cat are far more mundane.
In Episode 6, it is revealed that Nano is deathly afraid of cockroaches. It kinda makes sense that a robot wouldn't like bugs.
Nano is shown to be afraid of thunder in Episode 13. She's a robot. What normally comes along with thunder?
In addition, cockroaches have a tendency to hide in dark places. Like the insides of a robot.
This is half-Fridge Brilliance half-Wild Mass Guess: The Professor is afraid of dogs because she's scared they may bite her. Yet, her favorite animal is the shark, which is known for biting. This seems contradictory, but consider that the Professor is a scientist. A dog might bite her, a shark will bite her. It's not the dogs themselves she fears, it's uncertainty, the unknown variable.
Contrary to popular belief, most shark species aren't all that aggressive and won't attack humans unless provoked or by mistaking them for prey (especially if the would-be-victim is wounded). I wouldn't put it past her to not perceive them as a threat, especially since they can't live outside of the water.
Kids LOVE dinosaurs, but I doubt they wouldn't be terrified if they actually came across a REAL LIFE T-rex.
Nano desperately wants the Professor to remove the key from her back. However, the Professor always refuses to do so—not because she wants Nano to suffer for the sake of cuteness, but because she wants Nano to be accepted by others for who she really is.
The Professor's only eight, though... and the key is SO kawaii.
Considering how much landmass Japan actually has, it's not surprising for landowners to get a somewhat inflated attitude over their own place in society, which pretty much explains Sasahara.
The toast Helvetica Standard in Episode 5, when the toast hits the ceiling the lamp shook, and the lamp looks exactly the same as the one that fell on Mio and Yuuko's card tower much, much later.
You may wonder why Nano's so attached to the red, one-eyed doll and gets angry once the Professor ruins it. It's a Daruma doll - meant to motivate you. You fill out one eye (and the doll in question was like this) when you set a 'goal' and place it around your house to remind yourself of the goal. Once you reach it - you fill out the second eye. Since Nano's biggest wish is to be human she probably filled out the first eye thinking about this. No wonder she got angry.
The Professor 'ruining' it also has a bit of a symbolic value to it. Not only was the other eye filled, but both eyes were crossed out; Nano may have wanted to be human, but with her own emotions, desires, and everything; she not only had achieved that goal, but was *already* human, despite being a machine.
In the part/chapter where Yuko apologizes for stealing Mai's lunch, it is seen in the flashbacks that while Yuko was eating with chopsticks, Mai was eating with a fork. A bajilion chapters later, it is revealed that Mai moved to Japan from Alaska about a year ago.
The Fe Kingdom's symbol appears to be a square inside a diamond of equal size. ...Or is it a symbol of the two wooden cubes that are so important to the kingdom?
When Nano has a series of memories after she finally takes her key off, which results in her keeping her key anyway, one of the flashbacks involves Sakamoto calling her "girl" as he usually does. Not "robot" or even "robot girl"; Sakamoto knows full well that Nano is a robot, but still sees her as an (otherwise) ordinary girl.
The first real scene, and definitely the first part most people remember, involves Nano running into that kid and causing a huge explosion. Hence, the series LITERALLY starts off with a bang!
In a hilarious random side-scene in Episode 6, a random guy just got bomb-dropped. It's even funnier when you realize that Yuuko is probably still standing in the hallway. I feel bad for her, the world is too much for her to handle!
It's not some random guy, though. It's Sasahara, meaning the explosion is probably Misato up to her usual antics.
If Mio immediately regretted drawing Sasahara in front of Sakurai and Yuuko, how did it end up on the quiz? It would have to have ended up in Sakurai's possession in the end, and obviously Mio wouldn't let that happen.
But there aren't, at least drawn. And in Yukko's dream sequence they're able to be put on via vertical insertion.
Two halves, hinged, with a clasp or magnet on the other side.
In chapter 135 we see flashback of Mio getting her hair clips, and she doesn't know how they work either. At the end a hair clips vendor shows her the trick ("This goes like this, then you do this and then like this..." with his hands out of picture) — and that's about the best explanation we'll ever get.
I know it's a comedy cartoon and logic means nothing, but I can't help but wonder how Nano gets her shirts on through that big wind-up key. There's no visible seam or buttons in the backs and we never see her in the action of putting anything on over the key. Then again, we are talking about the creation of someone who could make a cat talk with only a scarf. Said eight year old was actually the one who presented Nano with her school uniform, so maybe she had to modify it first?
As of episode 24 we finally see the answer, there are buttons along the back of her shirt underneath the key. This info brought to you courtesy of the Science Teacher spying on her changing for gym.
If you look at the book Nano is reading in episode 11, the title is "Dostoyevsky". While it's certainly unclear which work would that be, does this add anything to her smarts?
The trio of Misato, Weboshii and Fe-chan seems like an imperfect derivative of the main trio of Mio, Mai and Yuuko:
Misato vs. Mio: Both have violent tempers, both have crushes on Sasahara, and they are the only two students in the anime with confirmed siblings.
Fe-chan vs. Yuuko: Both are optimistic, both get hurt a lot and often have their jokes backfire, and they have similarish haircuts.
Why does the Professor live only with a robot she made and a cat she found? Where are her parents/legal guardians?
In Ch. 124 of the manga, it begins with the Professor reading a picture story about a newly-hatched bird, who looks around, but no one is there (ie, its parents). She gets VERY sad over this and goes to curl up around Nano. Perhaps the story hit a little to close to home?
Although, in the flashback in the OVA, she looks like she's a little younger, and in Ch. 172 of the manga set eightish years in the future, she looks older. However, it could just be her hairstyles.
The Helvetica Standard in Ep.18 stands out in all of them for being very different. Not only is there a beautiful Art Shift, but the tone is also quite sentimental and nostalgic. When the book the girl was looking for turned out to be emptied out and was hiding a gun, this initially seems like a Funny Moment. However, this scene can easily be interpreted differently that turns it into a massive "Funny Aneurysm" Moment. The girl did not seem surprised when she found the book, and in fact, she stated that she wanted this specific book, not any other copy. If she did indeed know there was a gun in this book, what do you think she meant by "it brought colour into my grey childhood"?
Also, the name of the book is The Colour of Autumn: red.