I don't know how the Serbian girl learned English so quickly, but I do know the secret of the Romanian boy. He sat before the television set all summer and binged on "Happy Days." He literally learned English from the Fonz. Well, we all know (or anyone over 40 knows) what the Fonz would say to that.
Learning language from television shows is now recommended by various pop polyglots including Paul Noble and Gabriel Werner. Their suggestion is to watch shows you already know and loved--wildly successful shows including 50 or, better yet, 100 episodes--dubbed into the language you are learning. Noble, whose super-easy Italian materials I am reading, suggested Friends.
I never watched Friends. Squinting into the past, I see that the only shows I watched even semi-regularly were X-Files and Babylon Five. From 1996 to 2009 I didn't own a television, and when at my parents' I deplored my mother's love for Buffy the Vampire Slayer and other gorefests, shutting my bedroom door firmly upon the shrieks and moans of horror and pain coming from the living room TV.
But in the 1980s, my show of shows was Scarecrow and Mrs King, and to my joy, I have found it dubbed into Italian on youtube. I haven't found it for sale as yet, but Youtube fits the bill.
Polish is more complicated because the Poles do not dub foreign-to-them shows. Traditionally they have a reader (or lektor) reading a Polish translation over the original dialogue. Meanwhile, unlike the Italians and the Germans, they never developed a love for Scarecrow and Mrs King. This is without doubt because of timing: a show in which the baddies are usually Soviet spies was never going to be shown in the People's Republic of Poland.
The Wall came down in time for the Poles to see Friends, however. Here is a lektor reading along to Friends.
You may perceive the problem. It's even worse here with Big Bang Theory:
Thus I am as yet unsure as how to best improve my Polish by binging on television shows. It is all their fault for loving lektors so much and turning up their noses at the wonderful art of dubbing, which was perfected, I'm told, by the Germans.
Update: I have been reminded that Disney films for children are dubbed into Polish. This may be the way forward. There may be a Polish Disney Princess binge-viewing in my future.