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.
Darkness-Induced Audience Apathy: Since the people in the show, up to and including Malcolm himself, have a tendency to be jerks, it can be hard to care for them.
Dude, Not Funny!: Steve Fleming's ill-advised Josef Fritzl joke goes down like a lead balloon. When Olly is making the "eeeesh" face at you, you know you've gone too far.
Similarly, Adam shushing Phil's bad taste remarks after the news of Mr Tickel's suicide. Adam wasn't above mocking Mr Tickel when he was alive, but clearly considers Phil's behaviour to be a bit beyond the pale.
Olly isn't above these either. There's the time where mocks special needs children... in front of Glenn, who has a special needs child. And keeps going after Hugh calls him out. When he mocks Glenn over Malcolm punching him in Season Three, saying Glenn being "not technically a woman." Malcolm shoots Olly a Death Glare and tells him to zip it.
"You know Julius, if I wasn't a heterosexual man, I would kiss you."
That onion bhaji didn't solely represent the 'problems' caused by Nicholson's upcoming report. Julius becomes positively lascivious when Malcolm is about.
...and in turn Malcolm tends to get physical with him: "Put your hand on mine! Try and open the door..."
At home Nicola Murray struggles with a failing marriage to a husband who doesn't pay her much attention and never seems proud of her. At work there's a man who takes a great interest in everything she does and gives her his undivided attention... alright, it may be Malcolm but you can't really blame her for developing a crush. Most of their interaction involves Will They or Won't They?.
Hugh's comment to Olly about not "clicking" with the PM's wife (his assertion that she'd say "he's a social spastic and very probably a registered nonce") combines this with a good measure of Hilarious in Hindsight for those of us with particularly dark senses of humour, as Langham was later convicted of downloading child pornography. This indeed adds a painful note to any reference to public scandal or disgrace in the series, and there are plenty.
In Episode 3.1, following the "I AM BENT" incident, the staff brainstorm words that politicians shouldn't stand in front of, starting with anything containing the word "cock". A few years later, David Cameron did this.
Olly's on-the-hoof suggestion of announcing a spare bedroom database in S1E1 is not so far from a recent policy put forward by the government that would result in a cut in benefits to people who have spare bedrooms in social housing.
Cuts to government funding for school lunches were floated shortly after S4E2 aired.
The fact Peter Capaldi is now the 12th Doctor instantly has rendered large parts of the series into this. The "We've fucking time-traveled, yes?" speech likely being first and foremost.
Nicola's offhand Doctor Who remark, followed immediately by Malcolm looking uncharacteristically chipper.
The Missing DoSAC Files contains a letter from a TV exec pitching a Malcolm Tucker-led chat show where he interviews various interesting people. The photoshop depicts Malcolm interviewing a Dalek.
Magnificent Bastard: Malcolm Tucker, whose in-universe reputation precedes him. The Prime Minister's Director Of Communications is aggressive, foul-mouthed, unscrupulous and manipulative, but the most frightening thing about him is his charm. He constantly abuses it to get away with All Of The Above. Xanatos Speed Chess is his job, and the second special is a long game of it which he wins, naturally. He becomes more worn down by Series 4.
Olly Reeder: "He's impressive, Malcolm, in an evil way." ... Hugh Abbott: "That was quite Tuckeresque, really very Malciavellian"
Memetic Mutation: "Omnishambles" was named the Oxford English Dictionary's Word of the Year for 2012.
Misaimed Fandom: The show's cast and crew aren't necessarily flattered by its popularity with British politicians, especially those who've adopted it as something of a how-to guide. Will Smith (Phil) professed to be baffled when actual MPs started using the phrase "omnishambles" in Parliamentary debate.
Subverted. Olly goes through with it, but does it so that most of the bad press is focused on Glenn's behaviour rather than Hugh's.
Malcolm was always a cruel and nasty man, (particularly in the movie), but his cruelest moment of all time may well be in the final season, where, after manipulating Glenn in his plot to destroy Nicola, he turns him out when he is trying to come back.
Ship Sinking: Many people enjoyed the Will They or Won't They?Foe Yay between Malcolm and Nicola in Series 3, but in Series 4 Malcolm deposes Nicola as party leader, and then gives such a vicious "The Reason You Suck" Speech (which he delivers calmly and spitefully rather than loudly and angrily,) that we can safely assume that any love/hate dynamic between them is now just pure hate.
Stop Helping Me!: In retrospect, Malcolm's idea of turning Duggan's scrotum into a muppet and using it as the party mouthpiece would have worked a whole lot better than allowing Duggan to continue helping them, if only because the muppet might be able to function more effectively.
Tear Jerker: Malcolm's speech to Ollie in the final episode about how his job has destroyed any chance of him having a personal life.
Malcolm: "I'm as dead as fucking two-tone. But I can fashion my own exit."
Ollie: "What, you're gonna fly yourself to Switzerland and have a wank off a nurse and a bye-bye pill are you?"
Malcolm: "Funny, funny man. Political exit. I'm going to leave the stage with my head held high. What you are going to see is a masterclass in fucking dignity, son. The audience will be on their feet. "There he goes," they'll say. "No friends, no real friends, no children, no glory, no memoirs." Well, fuck them."