The pay phone definitely reveals you're dealing with an old Law & Order episode. But it's not an anachronism. Law & Order doesn't purport to display a period of time different from the one in which it was made. When you watch a 1990's Law & Order you see the world as it was in the 1990's. For it to show a scene where someone bums quarters for a pay phone is no more anachronistic than it would be for a film/tv-show depicting a scene from the 1890's to show people riding around in a horse and buggy.

Much different when you're watching a 1990's film that purports to display life in 2020, 2050, or 2100. Then the use of 1990's technology in the film is a true anachronism.