The hinges are easy to rebild, if they have play it is probably them. Ony thing,to rebuild them you will need to take them off the door and car to do it properly, before you do this mark very well the position they were mounted on as these are buggers to align afterward. Most Mustang shops sell kits for rebuild including the bushings and pins, makes all the difference.
69 Sportsroof, 351C, 4spd toploader, Restomod BOSS 429 clone - the one and only (?) 1969 BOSS 351
69 door hinge pins and bushings are a fairly universal thing. You can usually match your old one to replacement ones at a local NAPA store. I have even found them at [dare I say?] a local GM dealer! If the hinge holes are worn oblong, you will have to go to an oversise bushing. Good luck.