This show actually has been extremely realistic in that it's always the smallest, most harmless details that wind up catching hardened criminal minds. It's always the thing you expect the least that comes back to haunt. That's very realistic, actually.
On the contrary, I'm actually very picky when it comes to shows. Clumsy details that are ignored drive me nuts. Breaking Bad is ten times better at these details than most all other shows on television. That's precisely why I like it. It's not that I try to ignore those things. It simply doesn't have those moments like other shows do.
I've been a writer for 10 years. I've wanted to get into screenwriting, like you already are. And this show is the kind of writing I aspire to write because it's pinpoint on those things.
I saw a critic the other day that said this show has a "brutal honesty" about its storytelling. I find that to be absolutely true. Unlike most dramas where they suspend reality to bail out characters, this show really doesn't. In real life, most of the bad guys are eventually caught; even the ones that are great at covering their trails, eventually slip up in the smallest way. This show has been pretty on-point with that kind of storytelling.