The English title of the humming song is "I'm Human", which explains why Mechazawa likes it so much.
Kamiyama failing to notice Takenouchi, the largest human character in the cast, and ending up sitting on his lap as a result. This scene is like any other Out-of-Character MomentPlayed for Laughs until you notice that Kamiyama has his eyes closed for most of the scene. Kamiyama is the smartest member of the cast, so the scene may be a Deconstructive Parody of Eyes Always Shut, a trope often applied to wise characters.
Fridge Logic: Wait, why is Yamaguchi's first name (Noboru) written in katakana if there is a kanji symbol for it?
Memetic Mutation: It's become a running joke that every time anything Mechazawa related appears, people will post comments jokingly expressing confusion about there being something peculiar about that delinquent...
Padding: Whenever Kamiyama is confronted by authority while riding motorbike Mechazawa, there is a montage of moments from the current and previous episodes. The background music is awesome but it still looks like you're waiting for the punchline — which is odd considering all episodes are around 12 minutes, rounding up and including intro and outro music.