Contrails
Concorde would produce contrails in the same conditions that a conventional aircraft would. I've seen pics of it contrailing in supercruise, and it's a big trail.
Outbound, for reasons of best efficiency, the subsonic cruise would be at FL260 or 280 so contrailing was unlikely, but I would expect the occasional contrail inbound (cruising in low- to mid-30's) so you were unlucky not to see one if you were looking at the right time.
It would have been no more or less visible on primary or secondary radar than other commercial types.
It would be hard to see with the naked eye, unless the sun was reflecting off it.