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.
Red Sophia gives up fighting by the time she marries Cerebus.
Cerebus can be seen to go through this as well, but where it happens is debatable.
Broken Base: Many fans of early Cerebus disliked the direction it took with High Society and Church & State. Many fans of High Society and Church & State disliked the direction Cerebus took afterward. There's also the debate about whether Dave Sim's anti-feminist views are misogynistic, misunderstood, accurate, or irrelevant to the comic.
Creator Backlash: Dave Sim himself has come to dislike some aspects of this comic. In particular he regrets how he portrayed feminism and the female characters in general, feeling they were overly idealized/simplified and unrealistic. His contributor Gerhard hated working on the thing in general as he slowly lost any ability to read it and was overworked to exhaustion. He motivated himself to work on The Last Day by repeatedly reminding himself that he would finally be done with the comic.
Darkness-Induced Audience Apathy: The Church & State arc. The few sympathetic characters present (Michelle, Storm'send, The Regency Elf, etc) are quickly phased out; everyone who sticks around is either too amoral or too apathetic to really care about.
Designated Hero: Cerebus can be seen as this, since nearly everything he does is for his own selfish gain.
Designated Monkey: Dave Sim did this a lot as Cerebus went on, tying into his Creator Breakdown. Due to his rising misogyny, he hated pretty much all his female characters and generally wrote them out to replace them with Straw Feminist shrews. This, however, is nothing compared to Cerebus himself. A good part of Minds is devoted to Dave forcibly making Cerebus realize what an asshole he is and how totally unfit he is for human company. Pretty much the entire comic from that point on (about 100 issues or so, depending on where you think this begins) details Cerebus' slow and gradual self-destruction.
Growing the Beard: Happens a few times. Firstly, after Dave tripped out on LSD and created the first "Mind Game" issue where the comic began to have an actual plot. Also when Gerhard came in to do the backgrounds and inking, allowing Dave to concentrate more on what he liked doing and increasing the quality of the artwork dramatically.
Iron Woobie: The real Cirin has been through a lot. She was betrayed by her best friend; her peaceful movement morphed into a violent, fascist mockery of what it used to be; her mouth was sewn shut (which scarred her lips); she was placed under permanent house arrest; yet she bears it all with a smile.
Cerebus, after the events of Church & State. He pretty much stays this way for the remainder of the comic. Despite all the horrible things he's done, you can't help but feel at least a little sorry for him.
Jaka throughout Jaka's Story. She has an abortion because she thought a baby would make her ugly, and treats both her husband and Cerebus very badly but in the end your heart still breaks for her.
Marty Stu: Rick is the only character the author deems worthy of Heaven.
Pope Cerebus killed an infant and an old person to shock the crowds.
Jaka's abortion is clearly intended to be this for Rick in-story, and possibly for the reader, especially in light of her telling Cerebus in an earlier issue that she feared having a baby would make her ugly.
Serna betraying her friend Cirin and stealing her identity.
Padding: In one issue, 4 pages are devoted to Cerebus taking a piss. Dave Sim seems to find this sort of thing incredibly amusing.
Protection from Editors: Cerebus was self-published. The closest thing Sim had to an editor was Deni, and when she quit, well, let's just say that no sane editor (and not many of the insane ones either) would have allowed Sim to do the things he ultimately ended up doing with the comic.
Uncanny Valley: Sheshep Ankh. He looks perfectly human, until you notice that his feet only have three toes. Also, in the author's notes for the phonebook of The Last Day, Sim revealed that he purposely played around with some of the lighting and furniture in Cerebus' bedroom during his talk with Sheshep to give the hint to anyone that noticed that there was something very wrong about Sheshep.
Red Sophia tearfully talks to Cerebus about their marital problems, not in the least bit noticing that Cerebus is in some kind of magical trance and has his head in a glowing sphere.
Jaka hears the reasons why Cerebus is being shunned by his hometown (namely, not being there for his father's death and funeral because he was running around with a woman), and then hits Cerebus with what amounts to "it's your fault for not doing what you wanted to do." He doesn't take it well at all.
What Do You Mean, It's Not for Kids?: Don't let the funny animal on most of the covers fool you. The first two phonebooks might be appropriate for teens, but gory violence, nudity, graphic sexual material, and other frankly "adult" themes run throughout the rest of the story arcs, not to mention the more controversial material.