Ditto w/rtz. That driveline vibration is most likely the driveshaft that was not put back on correctly and is out of balance. Take out the four pinion yoke bolts, rotate the driveshaft 180 degrees, then replace the bolts. I'd bet that will fix it.
You just did a tune up? What did you replace? Wires, plugs, cap and rotor, fuel filter are good start to replace. Check your plug gaps and that they are correct. Make sure your wires are not damaged, ie. burned by headers, and that they are seated on the plugs correctly and the cap. Did you put the wires back on in the correct order??? That is a good chance of being your problem. Maybe two of the wires are crossed or something. Go back and double check it. My 351 was running and idling a bit rough untill I changed all the above except fuel filter which had been changed a while back. Purrs like a kitten now. You might check and see that your TPS voltage is correct. Check the timing too. Your ignition coil could possibly be going bad as well.
Check and make sure that your tranny fluid is at the correct level. Also, your shifting problem might just be that they didn't line up the shifter correctly when they put it back on (if they had it off). Was the clutch cable re-installed correctly?
Hope this helps.
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1996 Mustang GTS <---Must sell. $10,900 obo