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.
Some fans also seem to like Masako and John together; an odd pairing given that the former only has eyes for Naru in canon and the latter is a Catholic Priest.
Rounding out the list is Lin/Madoka, which is very slightly teased in canon when Mai wonders about their relationship to each other at the beginning of the manga's Bloodstained Labyrinth arc.
Ho Yay: Invoked by Yasuhara in the episode just after he is introduced. When Monk teasingly insinuates that Yasuhara and Mai like each other, Yasuhara states that he does like Mai—but he likes Naru better, and he likes Monk best of all. He then admits that he's joking.
Later on, though, there is actualHo Yay between them, some of it perpretrated by Monk himself.
Monk: Yasuhara is among [the students to be cursed]. Do you think I'm not worried, too?
During the Cursed House arc, there is a scene in the manga where Yasuhara is trying to treat the large wounds on Monk's back. Monk accuses Yasuhara of being a pervert for trying to take off his shirt. The Ho Yay jokes continue for the rest of the scene.
Tear Jerker: The episode Silent Christmas. "Kenji made it home for Christmas..."
Also the ending of the Doll House storyline. In a good way. Happy tears.
Gene's death. Hearing it described it is terrible enough, especially since it's revealed in the final volume, after so much build-up to create our attachment to the "kind Naru". Then you remember that Naru, his twin brotherfelt and saw every second of it. But the worst thing is you can finally know for sure that Mai will not have a chance to be with him.