the reason it may only be spinning one tire in first, is because of a gradual increase in power, as opposed to more than likely you're "dumping" into second (quick release on clutch) causing more shock and who knows, i know it usually helped me get 'posi' as we call it
but soon 2nd gear won't be 'posi' and it'll be peg legging too...
its an easy fix, you need to order a traction lok rebuild kit (fords term) costs about 50 bucks, pretty easy to do if you're mechanically inclined at all.
i ordered mine from D&D for 46 bucks i think, and got shims, spline plates (steels), clutches, and then friction modifier, and a new pinion pin bolt thingy too.....pre- lock-tited!!!!
yeah, the stock differential was meant to make both tires spin like you want, except its designed to slip turning and such (without spin)-- yours is just worn out.
get that puppy rebuild, and crank some donuts (its easy to rebuild i and many other stangnet guys have done it)
p.s., make sure to shim it properly! don't wanna drop a C clip do ya?