For anime, what I'm most interested in are the characters and the plot. Usually, if a show doesn't do either of these well and is too episodic, then it's not my thing (though there are exceptions, i.e. Mushishi, Kino no Tabi, Yakitate!! Japan). Though I tend to be picky with pairings and fandoms, if I do ship or participate, I can become obsessed.
For live action shows, my interest lies completely in the episodic stories. I don't ship, I don't join fandoms. Though I might be very fond of the characters and their relationships, usually I couldn't care less about their personal dramas, and sometimes even feel that they get in the way of what makes the show great if they're given too much focus. This might be why I'm more drawn toward crime dramas than sitcoms or plot-based shows. For example, my favorite thing about CSI: NY is how they fully utilize the diversity of the setting to come up with interesting cases, and what I like most about Cold Case is the empathic storytelling and reenactments of various time periods (though I've started to get bored with that show since realizing they solve cases almost entirely through witness testimony).
I guess as a result I'm much easier to please when it comes to live action, but at the same time I'm not nearly as invested. For example, "OMG Recurring Character A gets buried alive by a serial killer!!" stories bore me to tears, but I can be moved to tears by the fate of a character who only appears in one episode. Even if a show messes up its characters and relationships, I can still be entertained. And if I cease to be entertained, I can drop a show easily.
Heh, I don't know why I make such distinctions... Maybe it's a matter of culture, or genre. Or that I'm squicked by RPF and live action seems closer to that than animation does (which is stupid, I know).
EDIT: Another common storyline I hate is "OMG Recurring Character B gets framed for murder!!" Ugh. CSI: NY played that card like three times already.