Moe: Whenever Barbara was shown covered in soot after cleaning their stove, half the male population of England would have fought each other for her.
Unintentionally Unsympathetic: Tom, for his selfish attitude. He can be extremely callous to Barbara and sometimes the Leadbetters too—when Margo and Jerry have a major row, all he can think about is how it affects his prospects for getting "his" spinning wheel. Even Richard Briers said he didn't like Tom very much.
Unintentional Period Piece: In "When I'm 65", Tom suggests to his bank manager that the bank give him a pension and in return the bank will get his house when he dies. The bank manager finds the idea ludicrous. Today, equity release is a thing.
Several instances of casual racism: Tom pulling "slant eyes" for a "Confucius Say" joke, Margo being horrified into panic at the thought of Asian neighborsnote to be fair this one is meant to be seen as a character flaw, as part of Margo's general snobbishness, but it's revealing of the attitudes still prevalent at the time and it's doubtful the joke would be used in this politically-correct age, and if you pay attention you can see that Margo has an apron with a racist caricature of a black person printed on it.
As The Young Ones so eloquently explained, the show can become very grating if you aren't overly fond of the upper-middle-class, vaguely liberal ethos that permeates the show, and is more or less demanded by the setting and characters.
In one episode, Barbara says that she doesn't want to leave the house for a farm because she's a weak, emotional woman, and Tom agrees that she can't help it, because she's a woman. As with the example with Margo above, the episode immediately takes the piss out of him by having Jerry reveal that Tom was practically weeping over the cabinets. But that either Tom or Barbara would treat this idea as a given is rather archaic.
Values Resonance: Self-sufficiency is no longer seen as the joke that it once was thanks to the modern popularity of green issues.
The Woobie: Barbara, especially towards the end when Tom starts to show his true colors.
