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.
Huntress and Catman (he was doing well until he licked her).
Oracle and Calculator once met without knowing each other and immediately began flirting.
I Am Not Shazam: "Birds of Prey" is not the team's official name, and was not even mentioned until issue #86. In later issues the characters also specifically said that it was not their team name when Zinda Blake continues to use it. However, the writers themselves often seem to forget this point, as numerous characters (Both on and off the team) refer to them as 'the birds' on a semi-regular basis, and the full "Birds of Prey" title makes an occasional appearance.
Before it was revealed to be a fakeout, the supposed deaths of Savant and Creote. In the same arc, Black Canary's initial theory that White Canary was secretly Cassandra Cain did not go over well with many fans as she had already famously been turned evil in the past with disastrous results.
That in itself turned into a major case of Fan Dumb in some instances when Simone tried to assure fans that "they didn't know the full story" when it came to Savant and Creote, all but directly stating that their death was a fakeout. Fans continued to insist that she was wrong for even implying that they were dead, which led to Simone, who had previously visited Scans Daily in particular to comment and participate with fans, to break off contact with them.
Another was when Ryan Sohmer of The Guttersmade a comment about the series "constantly re-launching" and "hoping it would find an audience"... only it has been relaunched as an ongoing once (not counting a couple of mini series and one-shots before the first ongoing) and the initial run lasted over 10 years and 100 issues and gained a devoted fanbase who made the new series a bestseller when it relaunched. You can guess how said fans reacted to being told they don't exist by Sohmer, especially once Sohmer's Yes-Man started fighting back. Sohmer did eventually admit that he was wrong.
Les Yay: Canary/Oracle leans perilously close to canon sometimes, and (According to Word of God) was originally supposed to lean even closer than the finished product appeared. Black Canary was once supposed to refer to herself as "75% heterosexual," leaving the other 25% up in the air. Sadly, due to placeholder dialog and script confusion it wound up "heterosexual to the bone", to Gail Simone's chagrin (it was not, as many speculated, due to Executive Meddling). Observe◊. This image even predates Gail Simone's run, being from the earlier Chuck Dixon years.
Renee Montoya, the second Question, who was canonically a lesbian, pretty clearly had a thing for the Huntress (who canonically was not), although the New 52 reboot happened before that storyline could really go anywhere.
One arc during the Simone era introduced the Katerina Armstrong version of Spy Smasher as an old university "friend" of Barbara's turned rival. The use of quotation marks around "friend" was in Barbara's narration, and there was a definite homoerotic tone to the flashbacks.
My Real Mommy: Despite being created by Jordan B. Gorfinkel, BOP is most associated with Gail Simone.
Oracle has an eidetic memory. Normally this is pretty handy, but it also means she remembers being shot by The Joker as if it was five minutes ago. See also the entry on Driven to Suicide.
Also, the reveal of the Big Bad's identity at the end of issue 12 of the relaunch: Junior. Anyone who's read Secret Six will understand why that name is so pants-wettingly terrifying, made worse by the fact that enough hints are dropped before The Reveal that those who have read it will probably at least have an idea, even if not consciously.
So Okay, It's Average: The series after the departure of Gail Simone. Unlike most series affiliated with one author the quality never descended into true inadequacy and there was never an en masse abandonment by its readers, but it never did regain that extra something that it had under Simone's pen.
The same has been said of Simone's return to the title with a relaunch during DC's 'Brightest Day' promotion. Despite the fact that Simone was saddled with some characters she's since stated she didn't particularly want (i.e. Hawk and Dove), the title was never quite the same.
They Wasted a Perfectly Good Character: Say hello to Starling. Considered one of the few positives about the New52 relaunch of the book and having a great dynamic with Black Canary - who had lost a key relationship with Barbara - Evelyn 'Ev' Crawford was fun and well-received despite apprehension about the reboot. So of course, the perfect thing to do with this brand new character was throw her under the bus by making her a traitor to the Birds for Mr Freeze, of all people, despite this making very little sense in light of what we knew about Ev before the betrayal. And she hasn't been seen since.