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.
The Chinese population of Birmingham seems to be there for both the police and the gangs to exploit. Though there is a nice bit of subversion in one of Arthur's lines in the first episode where he acknowledges that the Chinese have their own gangsters and should just be left alone.
The Irish are not treated well either, being portrayed as Ax-Crazy criminals.
Anti-Climax Boss: Billy Kimber is supposed to be a feared gangster, but he's actually more of The Napoleon. He has his mooks do his fighting for him and is dispatched by a single Boom, Headshot from Tommy with no fanfare.
Cry for the Devil: Subverted in-universe with Campbell - in 2.06, he tries to convince an extremely vengeful Polly not to shoot him after he's raped her, tortured her son, and tried multiple times to kill her nephew by playing to her romantically, saying they have a connection, his heart belongs to her, etc. Polly shoots him in cold blood without a second thought.
Foe Yay: Fans are already anticipating this between Cillian Murphy's Tommy and Tom Hardy's Alfie Solomons, largely due to the duo's real-life friendship and work history.
Hell Is That Noise: The clank-step that heralds Major Campbell's arrival, due to his walking-stick.
Jerkass Woobie: Arthur, who starts off as more Jerkass and ends up more Woobie.
Magnificent Bastard: Thomas Shelby, who plays Xanatos Speed Chess with his family, his associates, the police, the IRA, the Bolsheviks, rival gangs, and pretty much everyone up to and including Winston Churchill. And does it ostensibly to better his family and position, but also a good deal of the time for shits and giggles.
Campbell's Jack Bauer Interrogation Technique and frequent raids on the Bolsheviks should have been our clue that however upstanding he may act, he's actually a despicable person. He really outdoes himself in episode four, threatening Tommy that he'll bash him and his brothers' heads in, kill Ada and her unborn baby, and throw Finn into prison with child molesters, all in the most affable voice imaginable. And tops that by allowing Chapman, Freddie's Bolshevik superior, to be severely tortured and die in police custody.
Arguably Tommy's treatment of Lizzie in 2.06. Lizzie has turned her back on prostitution, partly at Tommy's insistance, is trying to better herself by becoming a secretary and has no desire to go back to her old trade. Tommy invites her to Epsom for Derby Day, only to reveal that he wants her to seduce Field Marshal Russell in order to isolate him so that Tommy can kill him. Despite promising that he will turn up and kill the Field Marshal before anything can happen, in the event Tommy is delayed and Lizzie is very nearly raped by the Field Marshal and left thoroughly traumatised by the ordeal. Though Tommy wasn't entirely to blame for the delay (the police had sealed off the area he needed to go), he pushed Lizzie into the situation in the first place, and going by John's remark to Lizzie later that "Toffs at the races are the worst", it's hard to imagine that he didn't realise it had the potential to go horribly wrong.
Narm: Some of the accents on the show, but particularly Sam Neill's accent, which is nonetheless also praised as accurate.
The slo-mo scene where the Shelby boys curb-stomp the Lees is unnerving, with the silent screams and shouts of the men and only the soundtrack playing.
The sudden onset of paranoia, fear, and PTSD flashbacks all three of the Shelby boys develop when they find that the Lees have left a bomb in the ransacked house. It could literally be anywhere, and then it gets *worse* when Tommy figures out where it is, and finds Finn playing in the booby-trapped car.
Something is really not quite right with the one IRA sympathizer Tommy meets with, screaming an IRA song in the Garrison and looking as if he might break the whisky bottle over Tommy's head. Not to mention being suicidal enough to threaten a notorious gang leader in his own pub.
Darby Sabini's introduction - having his goons beat Tommy to within an inch of his life, then opening his mouth, ripping out one of his teeth, and cutting his cheek.
As well as the continuation and aftermath in 2.02, with Tommy covered in blood, being taken to the hospital.
The attempted rape and beating of Ada from the same time period.
Alfie's violent outburst against a random Black Country recruit.
The Peaky Blinder's takeover of the Eden Club, their thugs beat the shit of any patrons, men and women, who happen to get in their way and Arthur brutally stabs the boss in the throat and face repeatedly with a broken bottle
Ship-to-Ship Combat: Season Two has kick-started the Tommy/Grace vs. Tommy/May wars, especially with the second season finale's revelation that Grace is pregnant with Tommy's child and that Tommy is planning on getting married. If the Tumblr fandom is to be believed, there is no third option or compromise possible.