There are troublemakers everywhere.

Literal

Troublemaker [topic-は] anywhere [at-にも] exist [emphasizing-ものだ].

厄介者 ('troublesome person, pest') is formed from 厄介 ('trouble, bother') + 者 ('person'). どこにでも ('anywhere') = どこ+に+でも, the combination of locative に with inclusive でも. ~ものだ here has its general-truth sense, giving a rueful or philosophical 'that's just how it is.'