While it might be a little awkward, I don't know why it shouldn't be correct. It's just a compound sentence (The police had arrived. The mob had turned nasty.) and both verbs are parallel (had arrived/had turned, pluperfect).
It's a past perfect tense verb. Or the police had arrived and the mob turned nasty. First the police arrived and then the mob turned nasty.
"The police had arrived and the mob turned nasty."