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.
Base Breaker: Dorothy Wainwright from Yes, Prime Minister; fandom is split as to whether she was the strong, politically minded female character that Yes, Minister was sorely missing (Annie, while a fairly strong character overall, was more of an everywoman), or a Creator's Pet who is constantly shown to be right about everything, and is able to quickly reduce senior civil servants to babbling idiots in a way that even the likes of Ludovic Kennedy couldn't manage.
Notably Claire Sutton, Dorothy's spiritual successor in the play and 2013 series is considerably less moral and while still brainy makes one or two huge mistakes of her own.
Hilarious in Hindsight: In "The Moral Dimension," Bernard tells Hacker that he's got a call from "Mr. Haig" in the communications room they set up in the Qumrani royal palace. While Bernard's message was actually to advise Hacker on the availability of Haig whiskey illicitly smuggled into the palace, it carries an extra layer of hilarity when you consider that the role of Hacker was taken over by David Haig for the stage play and 2013 series.
The Scrappy: Frank Weisel. Even leaving aside the thematic reasons as to why he didn't work as a character, most fans found him extremely irritating, and he didn't add much to episodes beyond giving exposition (which Annie or Bernard would instead give in later episodes) and a reason for Sir Humphrey to make a Weasel/Weisel joke.
Sequelitis: To say that the 2013 Yes, Prime Minister series wasn't as well-received as its forerunner would be a gigantic understatement. Common criticisms included:
Flanderization of all three major characters. Hacker became far more bad-tempered and ineffectual than the original version ever was, Sir Humphrey became so corrupt and such a megalomaniac that he seemed to become a posher Expy of Alan B'stard, while Bernard seemed to have degenerated from being idealistic and pedantic to being an outright Man Child.
Padding: The series started out as a stage play and retained broadly the same storyline, resulting in a lot of clumsy exposition dumps. In particular, the entirety of the third episode basically consists of just two scenes; firstly Sir Humphrey trying to manipulate Hacker for fraudulent expense claims, and then Hacker trying to do the same to Sir Humphrey for illegal usage of government credit cards.
Seinfeld Is Unfunny: Granted, classic-style Brit Coms are near-invariably ripped to shreds by television critics regardless of how well (or badly) they're written anyway, but still the series (and even the stage play) was accused of being laughably outdated next to The Thick of It.
Values Resonance: it's surprising how relevant some of the political issues explored in the show (though by no means all) still hold true in later decades. For example, one episode deals with upgrading the British nuclear deterrent to Trident, in recent years the issue has been replacing Trident; despite being set in the Cold War, it's portrayed as just as ridiculously pointless as many think it to be now. Other issues including government waste, data-gathering and privacy concerns, Britain's place in Europe... And, whilst it was said to draw more by way of examples from the pre-Thatcher era than its own time (Thatcher taking a much harder line with the Civil Service than Jim Hacker ever dared), it remained a big hit with the then-PM and her cabinet.