What makes a show dated and not a period piece?

[PsychoSniper]

My two cents:

If its dated, it was relevant when it was made, but after a few years stops mattering.

If its a period piece, its set in a specefic time period (even if that period was the current time when made), but it remains something people can watch and relate to enough to enjoy it.

caveat: the graphics/effects being dated are not fully connected to the entire work being dated, an old work with dated graphics can continue remaining relevant on the strength of the writing/acting, classic era Doctor Who and Star Trek TOS are prime examples of works with dated graphics.

 

[Hassknecht]

Well, a period piece is usually intentionally set in a specific time period and aims to depict said time period. Artworks (in the general sense to count books, TV shows, video games, whatever, all as general works of art) are usually influenced by the time period and cultural influences they were made in, even when they're period pieces depicting the same time period. I.e. the way the Wild West has been portrayed differently in pseudo-period-pieces from classic Westerns to Spaghetti Westerns, to Neowesterns. It often reflects a certain contemporary view on things. Same with war movies that evolved from heroic war movies to anti-war movies and then back to revisionist styles depending on the current outlook.
As such, almost anything can be "dated" in the sense that it reflects the period it was made in. Science fiction movies, the execution of special effects aside, are very often extrapolations of contemporary knowledge and very rarely predicted certain technologies and their applications properly. Few have foreseen the smartphone and its absolute ubiquity and use to the scale we have even now. Older works predicted neither the Internet or small personal computers. That makes them easily dated to certain periods.
But I guess "dated" more commonly means something feels explicitly obsolete and bad because of it. My guess is that something becomes "dated" when its artistic merit doesn't hold up against its contemporary influence when viewed at a later time. MASH still holds up because it was simply a good show with great characters and stories. It was a period piece that wasn't too coloured by its contemporary views since it just tried to be a good comedy with some serious drama sprinkled in.
80s action movies might be more dated in that sense since many movies of that era aren't particularly well done, and their contemporary influence is too strong and obsolete to be anything but "dated". See the difference between something like The Terminator and, dunno, Cobra or Death Wish. The Terminator is a very well executed film that shows its age in its special effects and contemporary setting, but is otherwise pretty timeless in terms of story.
Cobra or Death Wish are less well executed and much more influenced by its contemporary values, when Reaganism was in full effect.
So I'd say something becomes dated when the nature of its time of creation becomes a detriment to its overall quality.