Causing problems again and again, in a way that wears you down. The feeling is closer to annoying than to dangerous: a troublesome cough is one that will not go away, a troublesome student keeps interrupting, a troublesome neighbour keeps parking across your gate. Notice the 'keeps' in all of those — troublesome things are repeat offenders, not one-time disasters. You would not call a car crash troublesome; you would call the little rattle in the engine troublesome. The word sounds slightly formal or old-fashioned in speech. A British person might say it; most Americans in conversation would say 'a real pain' or 'annoying'. It survives strongly in writing, especially in news and academic English — 'a troublesome question', 'troublesome side effects' — where it lets the writer signal difficulty without sounding emotional. It also carries a faint tone of the speaker being patient and above it all, which is why it can sound gently disapproving when used about a person.