Base-Breaking Character: Dovewing. Whiny, shallow and annoying, or a flawed but ultimately compassionate and understandable character? You decide!
Common Knowledge: For a while, a common joke in the fandom was how Firestar was supposedly killed by a tree, when in actuality he died of his wounds and/or smoke inhalation. However, this misconception has largely died down and the only people who still believe it are new fans, who will inevitably be corrected whenever it's brought up.
Die for Our Ship: Cinderheart. The fans insist it isn't ship-related, but the way she went from being mostly ignored to being accused of being one of the worst characters ever created by people who ship alternative Lionblaze pairings right after the book that introduced the possibility of her and Lionblaze was released seems like too much of a coincidence.
Epileptic Trees: Who's the fourth? And who's the next leader?
Foe Yay Shipping: Hawkfrost/Ivypool. It's understandable: he shows up in her dreams, trains her, compliments her (and only her), she confides in him, says her made her feel special...you can almost forget that he's out to corrupt her and kill her Clan.
Mind Game Ship: Hawkfrost/Ivypool is full of this. He's trying to use and manipulate her, while later down the line she's out to spy on him and the rest of the Dark Forest. He later ends up trying to kill her.
Narm: For some fans, the scene of Cinderheart regaining her memories as Cinderpelt is this. Likewise, the scene of Cinderpelt's spirit separating from Cinderheart and flying away.
Daisy used to be hated for getting in the way of Cloudtail/Brightheart and for being a Hysterical Woman. Two arcs of Character Development later and she's become very well-liked.
Seasonal Rot: Omen of the Stars is generally well-agreed to be the lowest point in the series. Common complaints included plot points either being reused or not done very well, Arc Fatigue, badly-written romance, and boring protagonists (Dovewing and Lionblaze especially).
Jingo and her crew. A Clan-like group living in a Twolegplace and facing their own unique struggles while harbouring a grudge against Sol? Would be cool, except they haven't even been mentioned since their debut in Sunrise.
Hollowflight, a young RiverClan tom training in the Dark Forest because he got bullied was a fan favourite, but little was done with his character.