The first thing that comes to my mind is driveshaft length and angles. It not going to be easy to tell without some good measurement equipment. In the test drive if you feel vibration, "BINGO" there is a driveshaft problem. Don't just accept that "Oh it just needs u-joint" crap! Look at the welds done for the motor mounts, if the welds look professional then most likely the welder knew what he doing. Look at the wiring, if there are lots of taped wires and it looks unclean or clutter it's a sign there could be problems with the electrical system. Check all the lights, wipers, horn, heater blower and anything else electrical.
Find out what the original engine was. Check the cooling system, by letting the engine idle for 15 minutes, if it overheats at idle then there is a sign the cooling system is not up to grade for a 350. Check into the transmission oil cooler, did they use a radiator cooler or an external cooler. I recommend an external cooler.
dave