What issues would I encounter trying to mate an old Chrysler Torqueflite transmission to the stock rear end of a 1960 Ford F100?
Not much at all, you are going to need a new shaft anyway so take the the old Chrysler shaft and have them put the ford yoke on it or get a conversion u joint for it.
How old is "old" as 61 and earlier had cast iron housings whereas 62 on were aluminum and an alloy Torqueflite is heavy enough so I'd hate to think what an iron one weighs. Also up to 65 had the ball and trunnion output which most folks like to get away from. If you are happy with what you have do as Rodhotz says and just get the Ford u-joint on the end of tour shaft and you're right to go.
Actually the normal U joint fits if you have the right yoke on yer 9 inch. If not there was a big little joint used by Ford in thelate 60s and early seventies that will solve this often. Seems to me it was 68 to 70 or something like that. Don
How old a Torqueflite? Try to avoid the pot joint they are obsolete and replacements are hard to find.