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.
Canon Sue: Susan is based on Stephen Moffat's wife, Sue, making her a literal example. She tends to get portrayed as the Only Sane Woman but has a tendency to veer into Jerk Sue territory.
Freud Was Right: The whole show - note the fact that we've just listed every single trope with "Freud" in it.
Jane's "Jake the Snake" puppet:
Sally: Oh my god, it's a penis!
Fridge Logic: Which leads to a Crowning Moment of Funny. During the episode "Inferno," after Jane's very vague grasp of what vegetarianism is, we get this exchange between her and her therapist at dinner:
Jill: A vegetarian is someone who does not eat meat, you insane bitch. Jane: I get enough of that language during our sessions.
Realize that Jane is so screwed up, she has sent a licensed health professional so over the edge, she's insulted her repeatedly — even calling her "insane," which is not a word psychiatrists are generally fond of. It was our first major glimpse into how messed up Jane really is.
Jill: We agreed two months ago to end your therapy, it was going nowhere.
Jane: I thought that was just an exercise to help me cope with rejection!
Jill: No, that was rejection.
Hilarious in Hindsight / Harsher in Hindsight: During series 4, while Susan is coping with her pregnancy, the very vain Sally is very uncomfortable with the whole process. She mentioned in "Nightlines" how she doesn't really want a child, and mentioned how unsettling she finds it. In "Circus of the Epidurals," whenever Susan goes into detail about the actual birth, Sally faints and goes to her "safe place." When you learn that Kate Isitt (Sally) was actually pregnant during Series 4, it either becomes a hilarious in-joke from the people behind the scenes, or becomes unsettling to watch a pregnant woman face the gruesome truth about what's going to happen to her head-on.
Steve including Daleks among the things sofas are designed to protect from, given Stephen Moffat's later career.
A rather depressing example, but Jeff claiming his girlfriend Julia is dead is a lot less funny and way more depressing when this troper found out that her actress died of cancer two years after the show ended.
Seasonal Rot: Some believe the show went off the rails at the start of the fourth series, when Richard Coyle quit, Richard Mylan proved an inadequate replacement, and the Patrick-Sally relationship began to receive too much emphasis.
For this troper the real rot began in the third series, where the laughs were more predictable and less spontaneous then they had been before. Geoffrey Perkins leaving the BBC in 2001 (he was once described as an "enormous influence" by the Father Ted writers) may well have had something to do with this.
And if we get to know the reason behind Jane's eccentricities... oh, poor dear.
Woolseyism: The US remake is generally considered inferior, but when Patrick's political stance is discussed, making him a Republican and a George W. Bush supporter is actually a pretty nice (and in-character) touch. However it kills Sally's breakdown, as a big part of what broke her was being told that Labour was in charge, while the Tories were now the revolutionaries.
In the first episode, Jane's use of stockings to seduce Steve is turned into not wearing underwear. Even if they do mangle some perfectly good sentences by simply changing the word 'stockings' to 'no panties'.