What manners are specific to mahjong?
I beg to disagree with User545. Mahjong is drenched in formal--even ceremonial--aspects: The sorting of the seats, the selection of the first east, the building of the wall, the breaking of the same, the collecting of the tiles, the procedures of play, the vocabulary... To a person who grew up with the game around her or him many of these might seem commonplace, but to someone new to the game they appear remarkably ritual. And the way expert players seamlessly, silently and knowingly interact in smooth choreography under the same peculiar (and somewhat mysterious) etiquette is uniquely enchanting to those being introduced to the game.

Furthermore, each national variant of mahjong (Japanese, Taiwanese, Korean, Vietnamese, Malaysian, even the Western variants, like American, or the Chinese Classical game now played mainly in Europe, among many others) has variations of these formalities and rites, not just of rules and hands. 

For example, the most popular mahjong variant in Japan--riichi mahjong, which is played extensively in that country, across all ages, and which is undergoing a true renaissance (not only in Japan, but around the world, thanks to Japanese manga and anime)--is particularly adept at meticulously keeping this ritual aspect of the game. This aspect affects all forms of game traits, manners, and in-game behavior, all the way down to tile size, as well as their handling, and the body language of the players in doing so. 

In Japanese mahjong, there are particular ways to shuffle (if not using automatic machines), hold and handle the tiles, build the wall, arrange discards (in neatly disposed discard rows, exactly 6 tiles across and 3 down), etc. The rules of the game strictly legislate the punishment of deviations of many of these behaviors, especially the ones that lead to time being wasted in the game or the cancellation of a hand.

And it's not only in Japan that mahjong game play generates manners, rituals, and codified behaviors and vocabulary. Also, it's not only because of the central elements of play. Different regional variants introduce locally specific accessories (counting sticks, tile racks, chips, first-east and round-wind markers, tile pushers, dice, different indicators [horse-race chips, yakitori markers, 5th-player bettor]), all of which generate region-specific behaviors and manners around their use.



One more thing to clarify is a notion introduced by the OP: Mahjong is NOT an ancient game like weiqi (go). The oft-repeated bit that the game is an ancient invention of Chinese wise men, and that it was played by Kǒng Fūzǐ, is shameless marketing poppycock introduced by the American entrepreneur that brought the game to the USA. Some of its distant forerunners (in paper card form) date back perhaps to the middle ages, but definitely not to antiquity. The game, as we know it today, originated during the final decades of the Qing dynasty (mid to late 19th century) and spread to the world in the early 20th Century.