What does Mr Darcy refer to when objecting to Mr Bennet's "want of propriety"?

Question

In Mr Darcy's letter to Elizabeth, he writes:

The situation of your mother's family, though objectionable, was nothing in comparison of that total want of propriety so frequently, so almost uniformly betrayed by herself, by your three younger sisters, and occasionally even by your father.

Examples of the mother and the three younger sister acting gauche are not hard to find, but I can't recall an example of Mr Bennet acting improperly in front of Mr Darcy. What was he referring to?

(In the 1995 BBC adaptation, there is a flashback at this time to Mr Bennet interrupting Mary playing. The scene was a bit awkward but that was hardly his fault.)

Answer 1

Let's have a look at what Mr Bennet actually says to Mary in the passage alluded to in the question:

[Elizabeth] looked at her father to entreat his interference, lest Mary should be singing all night. He took the hint, and when Mary had finished her second song, said aloud,

``That will do extremely well, child. You have delighted us long enough. Let the other young ladies have time to exhibit.''

(Chapter 18)

While this leaves some room for interpretation of exactly how harsh he is, we do already know that he has quite a satirical tongue. Furthermore, the part "extremely well" marks that he thought that she has gone to some excess, and to "exhibit" is certainly not a good thing! Consider, for example, this passage a bit later:

To Elizabeth it appeared, that had her family made an agreement to expose themselves as much as they could during the evening, it would have been impossible for them to play their parts with more spirit, or finer success; and happy did she think it for Bingley and her sister that some of the exhibition had escaped his notice, and that his feelings were not of a sort to be much distressed by the folly which he must have witnessed

(Emphasis mine)

Mr Bennet's speech is not very civil, and not only insulting to Mary, but also to the "other young ladies". Not a thing that a well bred man should say. Any further doubt should be dispelled by Elizabeths reaction to what he said:

Mary, though pretending not to hear, was somewhat disconcerted; and Elizabeth sorry for her, and sorry for her father's speech, was afraid her anxiety had done no good.

Furthermore, there is also the following part, a paragraph later, when Mr. Collins has had his turn at making a fool of himself:

Many smiled; but no one looked more amused than Mr. Bennet himself [...]

Looking amused when someone is embarrassing himself is not a sign of good breeding, especially if the person in question is a relation. This point is also reinforced by what Elizabeth herself thinks after reading the letter referred to in the question:

Her father, contented with laughing at them, would never exert himself to restrain the wild giddiness of his youngest daughters

(Chapter 37)

Laughing at others is bad enough, but not to attempt to regulate the behaviour of your offspring is a serious dereliction of duty. Mr Bennet might be the most likeable father figure in Austen's finished works (hardly a tough competition), but he is like all others (Mr Morland in Northanger Abbey, whom we do not see much of, possibly excepted) still seriously lacking, having failed to prepare his daughters properly for adult life.