These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
This troper found season 2's opening to be this as well
Ensemble Darkhorse: The black Nyanko-sensei a god who was trapped in a Maneki-neko, much like Madara, except this one is black appears in as much official merchandise as Nyanko-sensei himself (meaning alot), despite only appearing once. He's also popular in fan art.
The fox spirit kid is surprisingly popular, and fans of him always say one thing about him: D'AAAAAWWWWWWWW.
Gen, the snow bunny-turned-bishounen who, again, appeared in only one episode.
Hozukigami and Fuzukigami. Or mostly just their extremely pretty masks, but it's also common to ship them together.
Secret Secret Keeper: Shigeru is implied to be have become this thanks to curse incident at his house. He easily brushes off Natsume wrecking the room and does not question it despite Natsume not being able to formulate an explanation behind it. This trait is possibly influenced by the fact that this accident carries much resemblance to the past and that he knows both Natsume and Reiko aren't exactly ordinary people. However, this trope is highly downplayed as he seems to not be completely aware of Natsume's powers.
Tear Jerker: This show is packed with them. The sensitive are advised to watch with a wad of kleenex at the ready.
And then there was that part in Episode Six where Natsume cries upon seeing the photograph of the Youkai girl he'd grown attatched to, finally getting to be with the human she had so badly wanted to meet all her life, if only for a few hours before she vanished.
Any moment where Natsume feels less like an outcast and more like he has a place where he actually belongs doubles as both this and a CMOH.
Episode 4 of Natsume Yuujinchou San, when the youkai haunting a tree drops down to give the revisiting Natsume a gentle hug.
Episode 5 of the same season when the little youkais watching over the sick Shin'ichiro try to cure him by making their own version of a stethoscope and the little youkai with its hair in a bun sorts of sings to him while shaking the end of the "stethoscope" beside Shin'ichiro's head.
Every goddamned episode.
Viewer Gender Confusion: Kogitsune (The Little Fox-child) is still young, is drawn as a generically cute child, has long, silky hair, and has worn a sun-hat with a pink ribbon and a long, white shirt that could be mistaken for a dress.