Personal recommendation from a previous customer is a good start, also I would check that the broker actually has the boat physical or has at least seen the boat in question, loads just list anything and everything they can get their hands on and have never been near the boat. You get a load of b.s. about how mint it is and rock up to find its a shed.
Somewhat vested interest in recommending Inwards but before we went with a broker for our second hand stuff we checked out everyone and they were by far the most professional of the lot. They look after everything from lift in / out, surveys, valeting, berthing, maintainance, repairs and all the sales docs and handover, they also HPI check everything. Cara is the girl on the document side and she is a fearsome woman when it comes to paperwork, hounds the bejesus out of me for all the paperwork before anything happens with a sale, still, nice to know everything is tickey boo when sale is complete.