Among western audiences, many points of traditional culture in modern Japanese media come off as especially strange in terms of both appearance and reference. It is important to understand as such that these are not simple examples of the tired old “Asian inscrutability” excuse (though they are often mistaken as such.)
One of the oldest points of traditional Japanese culture still alive and well (and continuing to confuse many foreigners) is manzai. Manzai is a duo comedy routine dating all the way back from the Heian period (from around 800 AD to around 1200 AD) in which one member plays the idiot (boke) and the other plays the “corrector” (tsukkomi).
Some common themes in manzai routines include the infamous head slap from corrector to idiot and repetition of a particular theme or line for comedy’s sake. However, even if the TV program is not a manzai act, a good deal of comedy is drawn from it.
As manzai has such a long history in Japan, it is only natural that it would be deeply engrained in Japanese comedy in general. You can see evidence of this in variety shows, dramas and Japanese movies. Kabuki theatre is also heavily drawn from in multiple mediums. Two of the most prominent are manga and by extension, anime.
The roots of Kabuki go back to the Edo period (around 1600 to around 1870) and relied heavily on the use of face paints, exaggerated monologues and over the top strutting and posing. These themes can be found all over in many anime both classic and contemporary, with battle scenes riddled with dramatic posing and heroic dialogue.
Additionally, main characters both good and bad often times have some unique facial trait or appearance that very obviously draws from the Kabuki face paintings of old.
An occasionally mocked point about anime in particular is long shots focusing on a characters face during times of great drama. While some of these instances do in fact have to do with slowing down the story so the manga which is being published at the same time has time to get ahead, a good chunk of this can be attributed to the tendency of this medium to emphasize drama like this to excite the viewer.
Finally, the last point falls on a more philosophical note. A concept made popular during the Edo period is “mono no aware” or “the pathos of things” is also a commonly used trope of Japanese media, and it became so popular that it has even found its way into many Western works as well.
Mono no aware is a concept referring to an awareness of impermanence and an ultimate understand of the pain and beauty it entails. A good example of this would be the symbolism of falling cherry blossom leaves, their point of utmost beauty being shortly before they die.
The idea that nothing lasts is often used in Japanese love stories, which very much so differs from more Western approach.
Where do you see traditional Japanese culture come out in Japanese media?