Regarding M*A*S*H, I keep forgetting that the show took place at a time then television was starting to become popular (I wonder how aware the army's staff was of the invention, as they'd been busy with war). I remember being surprised when I first heard there was an episode where the characters were interviewed for a TV documentary.
M*A*S*H had the misfortune of always serving Anachronism Stew: it was supposed to take place between 1950 and 1953, obviously, but there are few mistakes throughout the entire run of the show, such as the mention of various movies that weren't made until after the war ended; Radar reading comic books that were printed in the 70s; Hawkeye and B.J. and others wearing 80s style civilian sneakers; B.J. towards the latter half of the series with his shaggy 70s style haircut and "porn stache"... one thing that REALLY grabs my attention everytime was the episode, "The Long-John Flap", in the scene where Henry's appendecitis flares up, and he fixes himself an antacid drink... I swear, his water pitcher not only doesn't look like a product of the 50s, it doesn't even look like a product of the 70s, it actually looks like a modern-day water pitcher. That's suspicious.
Not to mention, because the show ran so long, there were also some conflicting dates throughout the series as well, such as some episodes with Trapper, Henry, and Frank taking place as late as 1952, then later episodes with B.J., Potter, and Charles taking place as early as 1950.
One other thing that gets me too is everybody remarks on the obvious aging of the actors, especially Alan Alda, whose hair went from jet black to salt-and-pepper, and people questioning why didn't he at least try to darken his hair, reasoning that Hawkeye couldn't have aged THAT much in three years... but I actually think that's a more realistic visual, because not only does war take an emotional and mental toll on you, but it would probably also take a physical toll on you as well, considering all the stress (understatement) that he was under, nonstop for three years straight, yeah, I would imagine that that would increase Hawkeye's aging process... I mean look at Obama, his hair went gray within his first year in the White House.