There are those comix purists who will complain that BoP violates "continuity". If the truth be known, that which constitutes "continuity" is in the eye of the beholder (At last count, there are over five -- and counting --different Batman "continuities" [Movie Batman, "Batman: The Animated Series", "Batman Beyond", "Justice League", "The Dark Knight", etc.] ). At last count, Superman has over EIGHT different continuities (radio show, TV shows ["Superboy", "Smallville", etc.], and countless cartoon incarnations -- in addition to the comics). This is to say nothing of the pre- and post-"Crisis" versions of each of these characters.
There are so many different versions of Batman and Superman and different eras that trying to please each and every comic fan out there is a nightmare and an impossible task for a screenwriter. There are some people who want to see this version and some who want to see this era and if the writers mix them up then all hell breaks loose in Comix Fandom. To attempt to satisfy the whims of each individual fan is to ask for trouble.
While the critics are marking off their checklists and tabulating how well BoP adheres to its "source material", they're missing out on a fun show peopled with some quirky and interesting characters (The Huntress holds the singular honor of being TV's first superhero to see a therapist on a regular basis!).
"Birds of Prey" is best enjoyed when judged on its own merits. In my opinion, it's a fun show that deserves a chance to come out from under the shadow of its comic book origins.
