"Our boss is annoying."
麻烦 means troublesome, not annoying. I've never seen 麻烦 being used in the context of annoying.
Yes, the proper word for “annoying” should be 烦人/恼人 (lit. “annoy people”) or 讨厌 (lit. “beg for dislike”).
Stating that a person is (很)麻烦 means that person is a troublemaker (“troublesome” can also be translated as 讨厌 ;-).