Obviously the story of a zombie outbreak isn't, but I mean things like the costume, props like swords and muskets, social structure being shown. For example the partly see through hats don't seem like something that could be made without modern synthetic fibers.
I haven't seen the series, so can't comment on the social structure. Overall, the costuming appears to be quite good. At least for Joseon Dynasty Korea, there are plentiful artistic sources for clothing, and surviving late Joseon examples (and photographs), and Korean movies/series set in mid-late Joseon typically follow these sources and have generally authentic clothing.
The hats are very much traditional, with the wide-brimmed version dating back to the 15th century, if not earlier. They achieve their transparency simply by having an open weave. The traditional materials used are horsehair and/or bamboo fibres, both of which are long, and a single fibre can reach from the inside of the brim to the outside. The individual fibres themselves are quite coarse.
For more on these hats, see National Research Institute of Cultural Heritage, Gat, Traditional Headgear in Korea, 2013: https://books.google.com/books?id=yEpvBgAAQBAJ
For more on traditional Korean costume: Kyŏng-ja Yi et al, Traditional Korean Costume, Brill, 2005.
As for weapons, the muskets look good. I haven't seen enough detail for swords to be sure, but they look OK from a distance. The classic mid-late Joseon single-edged sword looks rather like the Japanese katana, but differs in the details of the mounts/fittings. They are worn at the waist, slung from the belt (like a Japanese tachi, not like the katana worn through the belt; Chinese swords of the time were also usually hung from the belt in a similar way). For examples of Korean swords, and info, see:
These are from an exhibition by the Macao Museum of Art; this is the online version of the catalog, which was/is also available as a most splendid (and large) printed book. Swords 117-127 are typical examples of single-edged swords. Typical double-edged swords (112-114,116) are very similar to Chinese swords (the open-frame pommel seen on half of those examples is distinctively Korean, but the other swords could easily be mistaken for Chinese swords).
In one still from the series, one of the characters was wearing his sword on his back. If it is an extremely large sword, this could be a convenient way to carry it. This would not be usual for a shorter sword which could be worn at the waist.
The disease in the show (set in the late 15th to early 16th century) is loosely, loosely, loosely based on what was probably a 19th century cholera outbreak.
The hats ("gat") are quiet realistic. The actual ones were made from natural fibers like horse hair.
This bit from an earlier answer may be of interest.
The broad-brimmed hat you saw is called a gat (갓) and its made of horsehair woven over a bamboo frame. An all-black variant of it called the heungnip (흑립) was worn almost exclusively by the educated yangban scholars and officials who made of the elite of Joseon Korea (1392-1897), although similar hats were also worn by middle class people and artisans. As you can see, it can be made with fairly simple hand tools and some skilled labor.
Farmers and other lower-class people wore a similarly-shaped had made of straw or woven bamboo called the paeraengi (패랭이) .
There were also a variety of other hats worn as status symbols by elites.
Most fabric was made of cotton and woven in by small weavers or in private homes. Upper-class people could afford clothing made of silk or nettle fiber woven by skilled weavers.
Parts of Joseon Korea's textile industry was extremely sophisticated - Joseon weavers could use complex draw looms to create ornate golden fabrics and could use geumbak (금박) techniques to apply gold leaf applique on court clothing.
