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.
The anime does this to Jabberwock because it was supposed to be the last episode.
Fuji/Satan comes off as this to the point that barely anyone feels he was worthy of being the Final Boss of the manga; especially considering how quick his introduction, and defeat, was. Justified, however, considering that the manga was marked for cancellation during his arc.
Chapter 225 gives us the reveal that Oga has gone to America. While context is quickly given for this (the Solomon Company has their base there), the initial reveal is so WTF inducing because, up until that point, the audience have been lead to believe that he'll be going to the Demon World.* Hilda had just returned from a reconnaissance mission in the Demon World bearing news of the Company's location, Alaindelon gives the excuse that he's currently in an unspecified 'foreign country', which is the blanket excuse for anything demon world related, and the Solomon Company are, well... demons.
Brain Bleach: Alaindelon in a bikini. Or a girl's school uniform.
Broken Base: Himekawa as the third crest holder, especially for fans of Furuichi, who feel that Himekawa will thus be easily forgiven despite it being his plan that got Furuichi's soul ripped out in the first place. Some are holding out to see what happens, but others are already calling foul or saying it negates Himekawa's assumed Moment Of Awesome.
Crazy Awesome: Oga, the guy who convinces Alaindelon to teleport a polar bear into his room just so he can fight it.
Dude, Not Funny!: After the Demon Tissues Arc, we have the part in the Six Upstarts arc where the six pieces of Furuichi's soul are named after his most-hated nicknames. A lot of fans felt that showed some serious lack of respect for the character.
Ensemble Dark Horse: Because of the quirkiness of the cast, there are a lot of fan favorites, like Good Night Shirokawa, the Red Tails (especially Yuka), Azusa and Kazuya, the Shadow Group, Zenjuro, Isafuyu, Yolda, Lamia, etc.
Oga and Hilda are by far the most popular couple in the series, at least in the English-speaking portion of the fanbase.
In Japan it's Oga and Furuichi that are the most popular pairing. Not surprising, once you learn how Oga and Furuichi met, and they bicker a lot too.
Furuichi and Lamia. Despite the age gap, it's surprisingly popular among the fans, who think they nevertheless have great chemistry.
Kanzaki and Yuka have had enough moments together that fans just end up pairing the two. Their "bottle" scene during the X-mas contest pretty much sealed the deal. Acknowledged in-universe too.
Tojo and Shizuka because of their Childhood Friends status before going to separate schools. Similar to the above example, their scene together in the X-mas contest where the two acted out a "pretend date" sealed their fate in the eyes of shippers.
After her initial defeat, Agiel seems to be really friendly with Aoi to the point of temporarily defecting to aid Aoi after she was attacked from behind by one of Agiel's superiors. Later, while possessing Furuichi's body, Agiel took time out of a battle to hug her.
Fridge Horror: With the use of one arm, Oga was able to destroy an entire school with Beelzebub's power... so how much destruction would be caused if he were at full potential?
Hilarious in Hindsight: Aoi notes at one point that if Oga's rampages continue then the school would be destroyed. It happens twice.
In Chapter 203, Himekawa, sitting in a room with Takamiya and his entire court, tells Oga that his joining up with the Fallen Angels was all a ruse to get them to drop their guard and that Oga's rampage was getting in his way. Oga falls for it like the idiot he is, apologizes, and leaves. Come Chapter 217, and we find out that Himekawa was actually telling the truth.
I Knew It: Way back near the beginning of the fight with Takamiya, many fans guessed that Iris had joined, and possibly even led, the Solomon company, and was trying to bring down the Demon Overlord because living with him was just impossible. While these fans weren't entirely right, they were surprisingly close.
Like You Would Really Do It: Takamiya ordering Lucifer to kill Furuichi by ripping his heart out. His main-character status had a lot of the fanbase believing that the mangaka wouldn't actually kill him off so suddenly. Turned out they were right and he was confirmed to be Not Quite Dead in the next chapter.
Ship-to-Ship Combat: This tends to happen between OgaxHilda shippers and OgaxAoi shippers. A lot of people on both sides like to play nice, but a good number of people supporting either ship engage in Die for Our Ship and fan bashing.
Shipping Goggles/Anti-Shipping Goggles: These tend to be used a lot. Both ships tend to look at anything that happens as either fuel for their OTP or irrelevant. Here's an example: after Hilda is kidnapped, Oga goes with Aoi to train under Ikaruga Suiten. OgaxHilda shippers like to point out how Oga was doing all of this for Hilda, and how even Kunieda enviously acknowledged that fact, but they'll ignore or downplay the fact that Oga and Kunieda did get closer during their training, and there were numerous parallels drawn between them and Suiten and Saotome, who are Love Interests for each other. OgaxAoi shippers like to jump on the latter points, but ignore the former.