Wouldn't a dab of solder on each contact fix that right up?
Maybe, but lead and tin are not great conductors. I use a quad eutectic silver/copper/tin/lead solder that works well for this kinda stuff as it flows very well and conducts better than standard 60/40.
if you get a higher wattage iron (25-40watt) really hot, put a little soldering flux on the contacts. Then you whet the tip of the iron with a little extra solder, touch it to each pad on the ribbon. You have to make sure the solder really flows and just "tins" the contact. Any more than that then the ribbon cable might not fit as Duo-r has stated.