The entire series is brimming with plot elements that make a whole lot more sense the second time around (or third, fourth, fifth, tenth...), but one very subtle musical cue sticks out. When Naota's head opens into an N.O. channel, usually an instrumental version of "Advice" serves as the theme music, with a wailing guitar riff overlaying the music. But in the third episode, the background music's slightly different during its N.O. opening scene: it's the full version of "Advice", with Sawao Yamanaka singing rather than the guitar solo. That's the only time a different version of "Advice" is used. Pay attention to what the lyrics are about: rebellion against dysfunctional, overbearing parents. And, in that one scene, Naota's not the portal - it's Ninamori, who's overwhelmed by her parents' scandal. Usually "Advice" is the theme song for Naota's channel, but since it's Ninamori's mind that's creating the portal this time, the theme music for it's slightly different - and instead of the guitar solo, her version uses the lyrics, because they relate to her situation and what triggered her breaking point.
Everything in the show is either a metaphor for growing up, a symbol of childhood, or a consequence of either of those things. Well, plus the many random things, but in the context of those other things, they at least fit a little more.
All of the characters in the show are childish in some way. Naota's dad just does what he wants whenever, Grandpa is having his "second childhood", the teacher is a stunted spaz who can barely hold chopsticks (which is something every kid can do before leaving elementary school in Japan), and Ninamori puts on airs of being "grown-up and responsible" but actually doing things to fulfill her selfish wishes. Commander Amarao is obsessed with "acting like an adult", yet he continuously does things that make him look childish. Mamimi had her growth as a person forcibly stunted; it's strongly implied that Naota's older brother took her virginity before she was ready, and left her alone when he went to play pro baseball in America, thus leaving her with nobody but her ex-boyfriend's little brother to lean on and vent her sexual confusion. Even Naota falls into this category; as the story progresses, he learns some very important life lessons, including the need to be active in going after what he wants (an adolescent mindset), rather than merely waiting for things to come to him (as children do).
Then there's all the symbolism. Meet a pretty teenage girl with a nice body, feel like you've been blindsided and hit with a blunt object, next thing you know you've got this thing sticking out of you and it won't stay down.
The way the city Naota lives in appears to the viewer reflects Naota's state of mind. As a kid, all you ever know is the places you've been. You don't have any sense of the world outside your locale beyond what you read in books or see on TV. Random people out there don't matter; you probably can't look them in the eye anyway, so they aren't really distinct. Tall buildings are just things that have no meaning. The scenery reflects this: the definition literally stops and becomes a fuzzy beige mass outside the city, there's a fog everywhere (representative of confusion and lack of understanding), and there's pretty much nobody around except for Naota and the people in his life. Fast forward to the end of the series. Naota's in his brand new middle-school uniform, walking to school. Suddenly, the world is cleanly defined, there are people and cars, you see people coming and going through the buildings, and you can see more of the world in the background (which was strangely absent before this). It becomes obvious that Naota's way of seeing the world has changed.
In the ending, where Mamimi leaves Naota after saying "so long". It's odd, because of the way she reacted to not being around him before, and then suddenly being fine with not being around him. But she called him Naota, not Ta-kun like she had done for the entirety of the series. This signified that she had got over her love for Tasuku and had stopped using Naota as his substitute, meaning she could move on with her life.
In the first episode, one of Naota's shirts shows a right angle. It seems just like a simple math thing but in reality, it's what he think he is. He think he's correct or right and more mature than most of the grown-ups he knows.
The day-old bread that Mamimi took in the first episode has some symbolism. Ever since Naota's older brother left, she's stuck with Naota. Naota and the day-old bread are the same thing: leftovers.
Naota keeps saying, "Nothing amazing happens here. Everything is ordinary." Which sounds remarkably blind of him, until you realize the entire series is basically a metaphor for growing up. What could be more ordinary than that?