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.
Angst? What Angst?: Romana spent twenty years in a Dalek prison cell. This is never mentioned again.
Narvin's stolen lives in Series 4. Even allowing for the core cast's vitriolic relationships, his revelation in Annihilation is very easily taken and put aside.
Also any antagonist in any alternate Gallifrey in Series 4. Even Chancellor Narvin, though slightly redeemable by the end, slams into the Moral Event Horizon when he "encourages" Romana to work harder by telling her that he'll start killing slaves if she doesn't, and is happy to prove that he's being serious.
Probably doesn't help that Brax keeps pushing everything on her.
Ensemble Darkhorse: Narvin, who begins as an unsympathetic bureaucrat and ends as one of the only consistently good characters in the series. His general snarkiness helps quite a bit too.
Ho Yay: Narvin misses Brax. They even manage to NOT argue for a split second when Narvin comments on Brax's trick with the impulse laser.
Many, many fans see this with Leela and Romana, particularly when they go on their honeymoon visit a relaxation planet together in series two and end up temporarily swapping bodies.
Launcher of a Thousand Ships: Romana, surprisingly. She's been canonically paired with the Doctor, some variant on Romana/Brax is quite popular and a one-sided Pygmalion Plot actually becomes canon, Romana/Leela was one of the first ships to surface in the fandom, and Romana/Narvin has a growing contingent of supporters. Somehow, 'The Ice Maiden' has ended up as the fandom bicycle.
Magnificent Bastard: In his first appearance Mephistopheles Arkadian, a simple human con-man and arms dealer, manages to outwit all the Temporal Powers and walk away whistling. However, he later tries for a repeat performance and is outfoxed by Braxiatelnote Who is easily either this or a Guile Hero, depending on the mood he's in.
Nightmare Fuel: The horrifically mutilated Time Lord in Spirit and Pandora.
Strawman Has a Point: Narvin, and to a lesser extent Darkel, who are lampooned for saying that Romana is an ineffectual leader whose presidency will lead to disaster. It does, with the planet in ruins and overrun by zombies.
Though to be fair to Romana, the same people who insist that her decisions will ruin Gallifrey also tend to be the ones who, in their efforts to subvert her plans, end up causing everything to go wrong in the first place.