I have a problem that seems pretty typical on older Mustangs.
The doors close ok but they seem to close much better if you lift up on the handle pretty good while you are closing the door.
Seems any two door cars with those longer doors have that problem as they get a bit older. I know I had the same problem on a 1980 Trans Am I owned some years back.
Is it safe to assume that if I either replace or at least rebuild the door hinges that will fix the problem?
That may not be the first thing I would look at. When they are closed to they still line up right at the quarter pannel? If they are siting high you may want to try and lower the striker plate a bit to get them to line up, then worry about the hinges.
I've never really looked at the hinges on my 65 but I had an 86 Mustang than the driver's door drooped on after about five years and 100,000 miles. It had a worn bushing in the hinge. On that one if you lifted up on the handle you could actually feel the door was loose. You could kind of shake in up and down.
If you feel you need to rebuild the hinges, it is easy to do. There are kits that have the brass bushings, springs, and new pins that you cut to length. Lube em up and your done. I did mine, I had to cut the old pins out, wasn't too bad but I did notice a difference in the way the door opened and closed.
If it's not the hinges, the door/striker just may need adjusted.
Do the lines on the door skin match up with the lines on the rest of the body panels? If they're sitting low then rebuilding or replacing the hinges may work, you can also adjust them to some degree. If they line up and it doesn't want to close without some help look at the latch and striker plate as mentioned. Of course there's a high probability it could be a combination of things and nothing I've said applies, but it's worth a check.
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Door question - 
