A Boy and His X: The story of Ramsey and his dognote who is more than he appears is integral in several portions of the series.
Adult Fear: In an early issue Ramsey winds up in the hospital after finding her staff and shocking himself with it, and the incident takes its emotional toll on Kate.
Affirmative Action Legacy: Though she is unconnected to the previous Manhunters, Kate is the first woman to bear the title, and the Distant Finale shows that her son Ramsey, who is gay, will take the title as well. The same storyline also introduced a new version of Jade, who was an adopted Asian-American teen.
Anti-Hero: Kate mostly seems to fall into Type III, though she gets perilously close to Type IV or V at times too.
Bastard Bastard: Kate's birth father, Walter Pratt, who killed her mother in front of her when she was a baby. He was the child of Iron Mundro and Sandra Knight, and while the two did get married later, Sandra hid the fact that she was pregnant from Munro and gave the child up for adoption
Billy Needs An Organ: Kate is reunited with her birth father when he kidnaps Ramsey for an (involuntary) bone marrow transplant, since he is dying of blood cancer. He then finds out that Ramsey is not a match, so he tries to lure Kate in, who is. It does not end well for him.
Boxed Crook: One of the first things Kate does is recruit Dylan Battles (real name Rich), a former Mook specializing in technology, by reminding him that she got him off on a plea deal for giving her information about his employers, and it would be all too easy for said former employers to find him if he does not cooperate.
Category Traitor: When Director Bones refuses to send back-up to help Kate rescue a group of Mexican women from superhuman organ-thieves, she tries to guilt-trip him by insinuating that he has forgotten what color his skin would be, since despite the fact that his skin, muscles and organs are invisible and thus he literally looks like a skeleton, Bones is in fact a black man. He immediately tears into Kate◊ and essentially tells her that a person of color never forgets that, even if their appearance changes.
Double Standard: Writer Mark Andreyko remarked how people complained about Kate being "unlikable" when the book first came out, and this was his response in an interview:
I was like, she's no more unlikable than Wolverine. Is it because she's a woman you find that unlikable? My biggest inspiration for creating Kate was Helen Mirren in "Prime Suspect." If you haven't seen it it's amazing stuff, Helen Mirren plays a homicide investigator who is a drinker and a smoker and is bad at relationships and is this deeply flawed character. But because she was a woman we hadn't seen that before.
When Kate sees that the Justice League has shown up in her office her latte goes flying, but Green Lantern John Stewart catches it using his ring's powers and remarks that he knows how expensive those lattes can be.
This occurs again with one of Kate's assistants when Wonder Woman is in her office for a case. She catches the drinks and ice just because she didn't want there to be a mess.
Even Evil Has Standards: A major reason for Dylan's Face-Heel Turn. He has no problem building giant robot armor for people who want to rob banks and take over the world, but a 10 minute conversation with The Joker has him ready to turn over a new leaf.
Fag Hag: Kate, which she lampshades. Her paralegal Damon Matthews, who she is probably closest to of anyone in the cast, is dating Todd Rice, aka Obsidian, of Infinity, Inc. A Flash Forward also shows that her son Ramsey is gay and inherits her title.
Flying Brick: The suit is reinforced, and her staff allows her to fly.
He Who Fights Monsters: Kate is well aware of this trope, and in an early issue has a dream where she rescues Batman by shooting the criminals holding him hostage, and after she frees him he calls her out for being no better than the villains.
Hypocritical Humor: When she first takes Dylan to a restaurant he is about to light a cigarette and she asks him "You think it's wise to break the law in front of an officer of the court?" but when he asks her a second later if she wants a cigarette she accepts. Also counts as a Hypocrisy Nod.
Karma Houdini: It was seeing Copperhead become one of these that first inspired Kate to don the costume.
Lad-ette: Even before donning the Manhunter armor, Kate smoked, drank and had more balls than many of her male coworkers.
Left Hanging: Given the series' cancellation, this is to be expected. Even though Kate Spencer's continued in backups in 'Streets of Gotham, Kate herself also appeared in Birds of Prey, and the last two issues were a Flash Foward into the future, hinting that the problems were resolved, it still left several threads hanging.
The last plot hinted at, a serial murderer of Abortion Doctors, was only started, but cut off abruptly.
Dylan Battle's ties with the Joker.
Legacy Character: Though Kate is one of many heroes to call herself "Manhunter," she does not have any connection to the previous incarnations except for her staff, which was used by a previous Manhunter, Mark Shaw. Shaw later becomes a supporting character.
Long Lost Relative: During the series Kate meets her birth father, Walter Pratt, but the circumstances are not good at all. Later, she learns that her grandparents are Sandra Knight, aka the original Phantom Lady, and Iron Munro.
Los Angeles: In the original series, Kate is based out of LA.
Made of Iron: Even without the reinforced suit, Kate's noted as being tougher than average. This is probably because her grandfather is Iron Munro, who was also notoriously Made of Iron, and was in fact created as a stand in for Superman.
Mama Bear: Do not hurt Ramsey. If you do, you are in for a world of hurt. Despite this, she is...
Name's the Same: Someone is killing off all the surviving heroes named Manhunter.
No Smoking: Averted. She smokes like a chimney, and at one point lights a cigarette with her gas burner because she cannot find her lighter.
Parental Issues: In an early issue Dylan makes a crack about "daddy not taking you to the circus" and Kate angrily says that he should never talk about her personal life like that again. We later find out that Kate's father murdered her mother in front of her when she was a baby, and though she did not know this for years the trauma of seeing it is implied to have affected her deeply.
Pay Evil unto Evil: Kate is a firm believer that the supervillains of the world, if they can not be contained, should be eliminated. This has lead to some friction between her and other members of the hero community.
Self-Made Orphan: Kate winds up killing her own birth father after he kidnaps Ramsey
Superpowerful Genetics: Kate comes from a long line of metahumans. Her great grandfather Hugo Danner, grandfather Arnold "Iron" Munroe and father Walter Pratt were all superhuman. While Kate herself is not fully-superhuman, she is unusually strong and tough and it is implied that she is a borderline metahuman. Her son Ramsey inherits powers that easily exceed any of his ancestors. He is also an extremely rare fifth generation metahuman.
Taking the Kids: After their divorce Kate's ex-husband Peter got custody of Ramsey, though Kate still sees him some weekends. Early in the series after Ramsey's accident with her staff Peter gets a court order keeping her away from Ramsey and threatens to sue for full custody. She takes this as well as you would expect.
Thou Shalt Not Kill: Averted. Kate does not follow the standard superhero rules of not killing her villains.