This will mostly be about Harley Quinn's inability to understand what's actually going on around her, or at least her lack of interest in trying to understand. I'm not saying she's dumb, but she's dramatically less correct about the world around her than she thinks she is.
Harley is, of course, the narrator of Birds of Prey, and so she describes the events of the movie, also sprinkling in her perspective on other events and characters as she goes. The following are the big things she gets wrong for whatever reason, but wouldn't if she weren't thoughtless or biased:
- She claims to be the brains behind most of Joker's schemes.
- The only of Joker's schemes we see are quite impressive, breaking out of Arkham then managing to find and free Harley from a maximum security black site during Suicide Squad. Harley plays absolutely no role in them outside of doing what Joker tells her to do, if even that. When Harley later sets out on her own schemes, she goes in with little to no plan and only succeeds via her combat ability and, more importantly, dumb luck. There is no intelligence required for anything she does herself. That doesn't prove she hasn't had any good plans, but it certainly hasn't been demonstrated to be within her wheelhouse, and Joker clearly doesn't need her brains.
- When contemplating why Roman Sionis may want her dead, her list of potential grievances includes several things over which even someone as violent as Roman obviously wouldn't kill her.
- There are a few things on the list that aren't even reasonable possibilities - things that definitely do not bother him or things he has no reasonable way of knowing. Among these was the simple fact that she was female, which, as horribly as he treats women, he clearly treats them better than like-for-like men.
- She accuses Erickson, Montoya's boss, of stealing Montoya's credit for arresting Sionis' gang.
- Erickson DID arrest Sionis' gang. Montoya acted as a rogue vigilante and participated in a brawl that was none of her business, didn't call for backup, collaborated with a jailbreaker, a spree killer, and the most wanted woman in Gotham, then left the mess behind for someone else to clean up. She probably should have been fired and possibly arrested for this, but Harley seems to think it would be fair for her to instead receive the credit for Erickson's work.
Now, the point isn't that I don't like her. I think she makes a much better supporting character than she does a lead protagonist, but all this makes her a more interesting character. So many people think of her as so smart, while the writing makes her out to be a self-centered ditz who doesn't realize how wrong her narration is, whether through lack of interest or lack of intelligence, and the fact that this is hidden in plain sight makes the movie all the more fun.