>>63795465 (OP)He made plenty of errors. He didn't know his enemy well enough, first and foremost. The Romans had faced enemies which had given them difficult match-up problems in the past (the Sarmatians for one) and he shouldn't have been so arrogant.
He followed them into inhospitable terrain, strung out his baggage train which got picked apart by a more mobile enemy force, and left himself with the worst situation any general can have: having only one option which was to treat and rely on his enemy's good courtesy to even escape with his life.
The good generalship move would've been to proceed as Caesar would've proceeded: throw your Armenian auxiliaries at the Parthians until you get to know how they operate. Their lives are expendable from the Roman perspective so, better not to risk your own men. And then he should've advanced slowly, building fortified outposts along the way, encouraging the Parthians to be the impatient ones and try to fight a battle that would favor the Romans more: something around one of these fortifications for example.
Crassus was impatient. He felt compelled to equal Caesar and Pompey's military reputations and was in a hurry to do so. It was a mistake and he should've been a little more careful.