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.
Freud Was Right: At least the fans like to think so. Arguably, many examples in game are indicative of this trope.
Good Bad Bugs: The boosted speed trick, which makes exploration a lot easier.
Goddamned Bats: Some of the Toriningen. They don't kill you (really, nothing in the game can except gravity) but if they hit you, they'll send you to a secluded area that you can either escape by waking up or by using the Medamaude effect which takes you back to the hub.
This◊ novelty gag, which has absolutely no relation to Yume Nikki apart from sheer coincidence.
I Am Not Shazam: Thankfully averted; even those vaguely familiar with the game are smart enough not to call Madotsuki "Yume Nikki."
It Was His Sled: How to make Uboa appear, as well as his very existence, which ruins a fair amount of the shock of discovering him. Then again, he has a 1 in 64 chance of appearing, meaning that most will never see Uboa anyway unless they either get very lucky or they explicitly try to find him. It can still be very shocking, however, when trying to find him, failing multiple times, doing it more just for the heck of it, and he suddenly appears.
Self-Fanservice: Many of the characters are portrayed in fan art as cuter and/or sexier than what their sprites would normally suggest. Masada gets the most of this, but special mention goes to Shitai-san, who's supposed to be a dead body.
Ship-to-Ship Combat: If you don't ship Masada/Madotsuki, be prepared for a virtual shove-in-a-puddle. And the people who don't ship them are usually too busy shipping him with Shitai.
It's difficult to find femslash shippers in Yume Nikki, but there's a few people who enjoy Madotsuki/Poniko, or Monoe/Madotsuki.
The Dream VS Dream April Fool's is a mock dating-sim so everyone's ship needs get catered, hilariously so.
Fan-Preferred Couple: In addition, the Masada/Madotsuki ship tends to be pretty popular with fans despite the fact that the game has no dialogue.
True Art Is Angsty: The reaction to the unofficial Alternate Endinghere. The general response is that it not only undermines the themes of the game, but also the ambiguity of its reality. That said, it does have its fans.
Seccom Masada-sensei is often considered one as well, given where he resides: a spaceship in the middle of space, with no sentient company. If you take out your knife, he tries to get away from you. And then there is the table with two chairs, as if he would hope someone would come to him...