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.
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.
Complete Monster: Maro, introduced in #6. He purposefully drowned the children of Maria, the woman who would go on to kill herself and become the Weeping Woman, because his magic relies on the power of belief. Because people believe in the legend of the Weeping Woman, Maro intended to use that to keep Maria from passing on after she inevitably killed herself and transform her into the urban legend, and she would go on to steal and/or kill more children.
Internet Backlash: DC's refusal to let Kate and Maggie Sawyer get married, even though both had been openly lesbian for years now caused some BIG backlash on the internet and lots of accusations of Double Standard and homophobia. It was made even worse when it turned out that this had led to the current creative team quitting in disgust.
Tear Jerker: In #3, Kate is attacked by the Weeping Woman and subjected to Mind Rape. Recognizing what a threat this woman is, Kate returns to her apartment and tells Bette that their partnership is over in order to protect her. Bette presses her for a valid reason, to which Kate coldly tells her that Bette is nothing more than a glorified pageant queen who can never understand what really drives superheroes like Kate, because all she's ever lost is "a tennis match". Bette slaps Kate and tells her that she probably would've driven away her mother and sister had they not died, then calls her a control freak before leaving. When Maggie Sawyer shows up at Kate's apartment demanding to know why she was stood up, Kate starts crying in her arms.
Unfortunate Implications: Zig-zagged on the issue of Kate and Maggie marry. It's apparently not a decision driven by homophobia, but rather because DC editorial don't want their characters marrying... which in turn raises more unfortunate implications over DC comics views on marriage.