Aluminum Christmas Trees: Some readers have expressed disbelief that Kate would (or could) have any sort of positive opinion about the military after her dismissal under DADT, let alone still think of herself as a soldier, to the point that some think she should be explicitly antimilitary because of it. However, many real troops discharged under DADT did end up reenlisting after its repeal; while Kate didn't reenlist, her continued, overall favorable view of the armed forces isn't unprecedented for such individuals. Additionally, Kate was raised on an Army base by two career soldiers, which would obviously influence her views on the matter in a positive direction, something that tends to be true of real Military Brats.
Awesome Art: J.H. Williams III earned two Eisner Awards for his work in the initial Detective Comics run, and later won an Inkwell Award for the titular series. There's a buttload of amazing two-page spreads with outstanding panel layouts.
Some readers like Wolf Spider for being another addition to Batwoman's rogues gallery, for his striking but simple costume design, and for providing a fresh (if lower-key and grounded) storyline to the series. Others hate him for starting off Batwoman's Badass Decay (especially for how cheap his tactics are) and dislike his arc specifically because of how mundane it is compared to the supernatural elements that were present before.
The New 52 introduction of Nocturna also earned some ire; while the readers remaining after the departure of Blackman and Williams III were intrigued by the possibilities the character could have, once in play it left a particularly sour taste in readers' mouths as Nocturna's immediate actions basically bordered on Rape as Drama, ruined the Kate/Maggie relationship and generally felt poorly handled, especially given Andreyko was responsible for the immensely popular Manhunter revamp of previous years.
In "Hydrology", Bette is portrayed as a reckless and inexperienced vigilante who ultimately becomes Kate's sidekick, in spite of the fact that she has more experience than Kate and has been a vigilante for a lot longer, at least in terms of publication history.
In "Webs", the first arc after Blackman and Williams left, Batwoman has trouble fighting D-lister Wolf Spider (who has nowhere near her level of training) and gets pretty beat up. For reference, earlier in this same series Kate fought off demigods and took almost no damage. She was even able to defeat Bane after he punched her square in the face, and only got moderately bloodied from that and showed no bruising afterward. Even with Wolf Spider's use of fear toxin, his skill against Kate is a bit unbelievable.
Subsequent issues have Kate getting KO'd from a mook's sucker punch, getting dropped from a shotgun blast when her suit was previously shown to fully withstand machine-gun fire, and having trouble with personal issues that she seems to deal with in out-of-character ways; all these items seem out-of-place compared to earlier issues.
A common belief is that Kate regularly uses and carries guns, whether with standard ammo or rubber bullets. However, this is only true for the DC Animated Movie Universe, not the comics, and was popularized by Batman: Bad Blood. It's true that Kate owns several guns, is comfortable around them, and has fewer qualms about using lethal force than Bruce does, but the number of times Kate has even held a gun on-panel could likely be counted on two hands.
Another common belief is that Kate is always stubbornly at odds with Batman in terms of how they both do their job. In actuality, their only real disagreement is about the subject of guns and lethal force, which has occurred only a couple times. They otherwise get along pretty well and remain professional.
It's popularly believed that Kate has a wild, rebellious, anti-authority personality. However, in the comics this is only true during the several years immediately after she left West Point and before she became Batwoman. Bad Blood and the CW series in particular depict her this way, but in the comics Kate has consistently been shown to be mature and fairly reserved throughout most of her life, and was a highly dedicated athlete and cadet.
The Kane family is commonly described as frequently moving when Kate and her sister Beth were young, but this is not supported in the source material. They only underwent the fateful move from Fort Bragg to Brussels, and then Kate and Jacob later moved to somewhere in the Washington, D.C. area.
Misunderstandings about what West Point does (or even is) lead to some believing that it's the same as Basic Training and that therefore Kate is not that skilled. Though Kate did not graduate from West Point, she was there for about 38 months (out of 47) as opposed to Basic's approximately 10-week schedule, and excelled in the three areas of academics, physical fitness, and military skills to the point that she was assigned to the third-highest rank in the cadet hierarchy for her final year.
Kate's past as a cadet is commonly thought to have originated in Batwoman: Elegy, but it actually existed as far back as 52, the comic she debuted in, since Renee Montoya comments on a photo showing Kate wearing a West Point uniform.
Complete Monster: Maro Ito, from the "To Drown the World" and "World's Finest" arcs, is a former warlock who became a servant of the Medusa cult, planning to unleash monsters from Greek mythology upon mankind. Starting off by drowning the children of Maria Salvaje, thus turning her into the Weeping Woman, Maro goes off to create several more monsters and have them kill and kidnap young women and children, whom he used for Human Sacrifice. Manipulating Batwoman—Katherine "Kate" Kane—to help kill his master Christopher Falchion, Maro becomes the chief servant of Medusa and helps her free many monsters from the myths, who then proceed to cause chaos all over Gotham, killing hundreds. Later on, he assists Medusa in the summoning of Mother of all Monsters to bring the end of mankind.
Ensemble Dark Horse: Believe it or not, but the Kathy Kane Batwoman was originally popular back in the Silver Age, and many readers wrote in asking for DC to bring her back after she was removed from Batman's supporting cast during the 1960s.
Genius Bonus: While Kate only makes an explicit Kabbalistic comparison to the red of her suit, black would correspond to binah under this same logic, which is among other things is associated with deductive reasoning and repentance, concepts that are also relevant to her.
Given the heavy amount of Executive Meddling used on Justice League: Cry for Justice, it's probably a very good thing that Batwoman didn't have a stronger role in the story. This can be further strengthened by how universally reviled the series ended up being.
In Elegy, a flashback panel shows Kate wearing a t-shirt with the logo of Finnish goth rock band The 69 Eyes. About three years later, the cover of the band's single version of the song "Love Runs Away" featured a large red bat symbol on a black background.
Issue #18 shows a view from Kate and Maggie's new apartment, purchased in the wake of the destruction of Kate's penthouse in the previous arc. One of the buildings visible, and seemingly only a couple blocks away, is the distinctive Old Wayne Tower. This would later become the site of the Belfry in Detective Comics (Rebirth).
Cameron Chase's reveal as a lesbian in the Rebirth era provides a whole new dimension to her antagonism toward Kate.
Seasonal Rot: Some feel it set in when Greg Rucka left the book, but many felt Blackman and Williams did a good job continuing the story. Most will agree that those two leaving the book is where it went downhill. J.H. Williams's III art is sorely missed, breaking up Maggie and Kate is almost universally agreed upon as bad, and the conclusion to Mr. Bones's arc was rushed after being delayed for four months. Subsequent arcs by Marc Andreyko feel inferior both to the previous Batwoman issues as well as his other work. Some stories feel rushed, with numerous villains and plot points all vying for attention with little build up and often with unsatisfying conclusions. Other elements, like Killer Croc and the heroic Religion of Crime sect, have been dropped entirely. Kate also undergoes significant Badass Decay as she becomes less assertive and gets beat up by a couple of C-list villains who would ordinarily give her no trouble at all, with little to no adequate explanation as to why.
Ship-to-Ship Combat: Kate/Renee vs. Kate/Maggie. Fans will debate over which pairing had the better chemistry, which stories were better, etc..
They Changed It, Now It Sucks!: Inevitable with the change in creative teams. Complaints cover virtually all aspects of the comic: the writing is worse, the art is worse, the supernatural element is gone, and characters are no longer themselves, especially Batwoman herself, who went through significant Badass Decay both physically and psychologically.
They Wasted a Perfectly Good Character: The Kathy Kane Batwoman is viewed by many as a Damsel Scrappy who only existed for the sake of Batman having a girlfriend to dispel Ho Yay subtext. However, some readers believed she had the potential to be a good character on her own since her first appearance demonstrated she could be a competent crimefighter, had Batman not convinced her at the end to give up her identity for rather hypocritical reasons. That didn't stop her from becoming Batwoman a few more times, but her competency as a crimefighter was severely diminished.
They Wasted a Perfectly Good Plot: Though some liked the above-mentioned Crimes of Passion story for tying up some loose ends from the New 52 series, others were disappointed that the story involved a couple that had been broken up for years at that point, instead of being a more relevant romantic tale about Kate and her current partner Renee Montoya.
Unintentional Period Piece: A big part of Kate's story is being forced to quit the armed forces for being openly gay. A mere five years after the character was introduced (and less than a week after her solo series started), the United States dropped their ban against openly gay members of the armed forces.
Unintentionally Unsympathetic: Kate's handling of mentoring Bette comes across as somewhat needlessly harsh and unfair in regards to Bette. While it's true Bette is known to be somewhat flighty, there's the fact that she'd already been called out by Nightwing about "not taking it seriously" as a hero. This only caused Bette to reaffirm herself, getting a new costume and making more of an effort without losing her positivity. While Kate was obviously trying to drive Bette away to protect her, it's shown she had little to no faith in Bette's capabilities and her accusations of Bette "having nothing to fight for" comes across as cynical to the point of cruel; just because Bette hadn't suffered like Kate and a lot of other heroes didn't make her desire to be a hero any less genuine.
