Can TV improve your writing?
Absolutely, if it's The West Wing, Gilmore Girls, Buffy the Vampire Slayer, or (apparently) Breaking Bad and The Wire. I haven't watched the last two, but I understand from some of my writer friends that the writing in them is amazing.
TV-- especially, oddly, the music over action scenes-- inspires me. I've been watching The West Wing, and I couldn't get enough of it seasons 1-5; however, six kind of lost me. Took me almost the same amount of time to watch that one season as it did to watch the first five. And I'm seriously considering quitting with season seven. I still HIGHLY recommend those first five seasons, and I even feel they wrap up pretty neatly, so that six and seven aren't really necessary to your enjoyment of the show-- I mean, it won't leave you hanging.
Just to clarify, I'm a social conservative and an economic libertarian, so pretty much diametrically opposed to the stance of The West Wing writers, BUT. It's easy to get past that and just enjoy the cadence and chemistry of the show. Those first five seasons are pitch perfect.
So it's winding down, and I'm probably moving on to Breaking Bad next, but I'm always up for shows recommended by writers. They tend to be the best ones.