The first thing I would look out for is "rust". Mustangs in those years had a tendency to rust at the bottom of the doors. Water would get past the beltline, at the window, and pool inside the doors. Drain holes, found at the bottom of the doors, could become stopped up with an acumalation of dirt over the years. The results may be a very nice finish on the outside, but a very rusty finish inside the exterior door sheet metal. That same rust will find it's way through. Take a squint, with the window rolled down, between the exterior beltline and the glass frame to check the condition. Likewise, look around the fender "lips"/wells, behind the tire at the rear quarter, corners at the rear glass, and behind the back valence. Ask to see if you can have the door sill plates removed to inspect the floor pans. Another place for rust if the previous owner(s) like to shampoo their carpet alot. Check under the car for rust and to verify that the seat plugs are in place. If they are not, check around each unplugged hole (8 total) for rust. When you are sure of this then proceed to the next step.
To save a little money, from the get go, check to see how the car "tracks". Ask to have some water poured out in the street suffcient for a tire rotation each side. Drive through the water and over a dry area for about 15 to 20 feet. Check to see if the rear tires are in true line with the front by the tracks they leave on the dry area. If one is offset tell the seller to have a nice day. Chances are the car was involved in a very nasty side impact accident at one time and if it was you'll be buying tires for it now till doomsday. Besides just think how "goofy" you look in a car that goes down the road sideways. However, IF things look good here I would still take it down to check the "alignment" and "tracking" by the pros before buying the car.
Speaking of which "drivetrain". Listen to the sounds of the engine. It obviously should be voided of "ticking" or "tapping" sounds. Check to see if the engine is cold and, if so, let it warm up the way it is suppose to (in other words don't "blow the crap out of it"). As it does warm up check for any variences in sound. Remember, it is an old engine, so it going to sound different then a late model. If it sounds "tight" take it down for a mechanical insepction. Let them run the gambet on the entire drivetrain and, as long as it is in the air, the entire front end. You surely don't want any suprises.
Cosmetics. Look for body waves, by standing to each side front and back, and a couple steps out. You'll see them if they are there. Your choice for this type of inspection. But, since I show my Mustang and I judged some carshows, I wouldn't have "the waves". The rest "kid" is up to you!
68 Mustang Coupe...My Show Car. ............................