Why is it that some anime use language exclusive to the Yakuza?
The Introduction to Yakuza Japanese has a list of grammar, pronunciation, and vocabulary (and even lessons!).

There's also this Japanese Stack Exchange has a question: What are the stereotypical characteristics of yakuza speech?

And Japan Subculture's terminology page.

While Yakuza these days are mostly semi-legitimate, they still extort and is the largest criminal organization in the world. Just like how there's a taboo with tattoos in Japan because they're associated with Yakuza, the same connotations come with speaking like the way Yakuza do.