Steel or aluminum DS and what rear end gears? Reason I ask is due to what Mike eluded to in that it could be a critical speed issue. Typically you see Mustangs moving to an aluminum DS when the rear gears are swapped to 3.55 and lower gears. Again, I said typically as it varies from car to car depending on max rpm, tire height, trans gearing, rear end gearing, and the length of the driveshaft.
In case someone is not familiar with critical speed here is the mechanical definition:
An object is said to reach critical speed when the speed of its rotation corresponds to one of its natural frequencies. The natural frequency will vary with the type of material (steel, aluminum, carbon fiber, etc.), diameter, and length.
Modern DriveLine has a really good explanation of all of this here:
Common causes of driveline vibration-U-joints, slip splines, yokes, out-of-balance components.
www.moderndriveline.com
There is an equation to calculate the critical speed of your combination and then a chart that shows the critical speed of a driveshaft based on the material of construction, diameter, and length. I would look at this and make sure that driveshaft that is currently in the car does not have a critical speed that is lower than what is needed in all forward gears.
Check the pinion angle and if that is good to go then I would do these calcs and determine whether the driveshaft is good to go or not. If it is good to go then take it to a driveline shop and have them spin it up and see if it is out of balance, has bad u-joints, or a bad yolk.