Learn Italian: Il fumo mi dà fastidio.

In Italian, the concept of 'bothering' someone is usually expressed with the set phrase dare fastidio (literally 'to give annoyance'). So, mi dà fastidio translates literally to 'it gives annoyance to me'.

What role is mi playing in this sentence?

mi is an indirect object pronoun here, meaning 'to me'. Because the idiom is dare fastidio a qualcuno (to give annoyance to someone), the person being bothered is the indirect object. This is a common trap for English speakers, since 'bothers me' uses a direct object in English.

How could I apply this lesson's pejorative suffix to talk about 'nasty smoke'?

You can drop the final vowel of fumo and add the suffix -accio to create fumaccio (nasty, thick, or foul smoke). The sentence would then become Il fumaccio mi dà fastidio.

Why does the word dà have an accent mark?

The accent mark distinguishes the verb dà (he/she/it gives) from the preposition da (from/by). They sound exactly the same, but the accent prevents them from being mixed up in writing.