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.
From the movie:
Foe Yay: Balthazar and Lucifer towards Constantine. He's not liking all the hellish attention he gets.
Meta Casting: Keanu Reeves was a very... odd choice to play John Constantine, but as it says elsewhere, the movie is good if you don't mind its In Name Only connection to the comic book. So as long as the protagonist doesn't have to be a fast-talking cockney scouse Anti-Hero... who better for the role than The Devil's Advocate?
Mis-blamed: Connected to the above, Reeves is blamed for pretty much every alteration between the movie and the original source material, apparently solely based on the rumors that he couldn't do the proper accent. Casting Reeves was apparently one of the last things done for the movie, after all the other changes had already been decided on.
Nausea Fuel: Satan sticking his hands in Constantine's chest and ripping out cancer tissue.
The novelization is even worse, as it goes into some of the torments in-depth, such as the buildings being built from bricks that are actually damned souls (many of whom are inquisitors from the Spanish Inquisition among them), and describes Angela looking into the mind of the Scavenger and seeing herself being raped by him (Mammon had promised him Angela as a sex toy if he complied with his wishes).
For that matter, what exactly differentiates between performing a Heroic Sacrifice and Suicide? Constantine killed himself to save the world and he's saved by God. Isabel does it and she's condemned to hell? Made worse if we assume that Angela was always meant as the real target, but in that case, making a pair of twins psychic and both vulnerable to possession paints God as a massive dick.
In fairness, Constantine at one point refers to God as "a kid with an antfarm", which he certainly could be if people don't like how he plans out our lives. Certain elements of the movie could possibly be considered a Gambit (or some sort) by God, but it's still kind of jarring.
One's eternal destiny is sealed at the moment of death. The possession may excuse the suicide, on account of lack of control over one's faculties, but it does not expiate the act of divination that resulted in the possession in the first place. Isabel was damned not for suicide, but for divination.
Visual Effects of Awesome: This movie has the coolest looking adaptation of Hell seen in cinema thus far. And the demon made of insects looks particularly awesome as well.
Special mention goes to the scene of Angela getting dragged through the building by an invisible force. This troper remembers sitting in the theater when the trailer premiered, jaw on the floor, and agreeing with her father that she was sure as hell going to see that movie.
As previously mentioned under other tropes on this page, if you ignore the connection between the movie and Hellblazer, the casting choices are not so bad.
From the series:
Blooper: In the final scene of the pilot, the level of beer in John's glass changes from full to having a large sip taken out of it and back to full.
Broken Base: The show's getting a rather nasty one after it was revealed that John would not be bisexual in the show, as the creators deemed it unnecessary to his character. Unfortunately, they also added "And besides, he sleeps with mostly women anyways." While there are some who don't care (Citing how John's romantic partners tend to die in the comics, how he only ever slept with one man in the comics, or that they're gonna judge the show when it comes out and not before), a lot of viewers (most of whom are LGBT themselves) are upset at the bi erasure.
Nightmare Fuel: The opening scenes involve Constantine being given electric shock therapy... voluntarily. It ain't pretty.
The demons are nightmare fuel incarnate - especially the one that murders and possesses Liv's friend Talia and attacks the EMT in the ambulance. It shows off a lovely little bit of Body Horror later as well.
Liv's vision of her grandmother. At first she looks like a kindly spirit, but then she raises her head... She is eyeless, and lets out a horrific screech as both her eye sockets and her mouth begin leaking a viscous black fluid.
Tearjerker: When we learn why Constantine checked himself into the asylum - he was apparently unable to save a nine year old girl from being brutally killed by a demon. When the psychiatrist calls her "the girl" one too many times, Constantine leaps up and screams that her name was Astra, and that it's his fault that she'll never live her life.
The reveal that John accidentally allowed Astra to be ripped apart and dragged to Hell, and lost his soul in the process, all due to his overconfidence.
And then Furcifer attempts to use an illusion of her soul to trick John into releasing him, which begs to be allowed to go home and see her family again. Ouch.