At about 19:57 in S2E5, the gangsters give a dog cocaine by rubbing it on their teeth. The dog is all riled up and escapes the bar, they rub after it and we don't see it again. Cyrus explains to Sara and John that there will be dogfights that night at the bar. In Episode 2 at about 18 minutes of S 2 (this was already explained in another answer but im case someone wants more explanation) these same guys try to dogfight and Cyrus kicks them out of said bar. I hate this kind of stuff. Very unnecessary, but you can tell the dog is fine and anytime we see animals they're usually obviously fake. But this show is still very graphic so please watch with caution.
At 29:32 S2 E5 we see a bunch of a**holes in the street preparing for a dog fight. There's two dogs shown on leashes barking at each other and they start to talk about who is going to bet on this. By 29:50 (I looked away so I can't speak to what goes down during that time but it's probably a dog fight), the scene cuts away to a sex scene in the street. We are officially out of that scene at 32:16, so if you don't want to see any of that go down, skip to this time marker. (I absolutely HATE this stuff and wish people explained more thoroughly on this site when and when not to watch, so I hope this helps).
S1E2 ~46:16. It is heavily implied that (a drunk and drugged) Moore is assaulted in the Molly house / brothel. References to it are made in S1E3 in a conversation starting ~3:18.
Ep 1 early on, a child's body is found mutilated and missing various body parts including eyes. There is a close-up on the face with 41:02 remaining (I can't see time lapsed on my Netflix, sorry!). There is a painted depiction of the body shown with 36:44 remaining, the painting is shown again with 20:45 remaining and again with 16:00 remaining.
Ep2 with 37:49 remaining a scene at a butcher where an animal head is having its eyes removed
In season one the main character (Laszlo) purposefully injures his disabled arm (hits it against a piano multiple times in S1E7 and breaks a glass and stabs his own arm in S1E9). I have no idea why no one has labeled this as self-harm before. NOTE: I haven't seen all of season 2, so I don't know if it continues.