our stock diffs are torsen diffs which means they are TORQUE SENSING LIMITED SLIP ("TORSEN LSD").
Im about 80% sure that when you jack it up, it will not turn one wheel when you turn the other, to test the LSD, do one of the following...
1: when raining, warm up your car and then have some one stand on either side of your car and do a burnout, if both wheels spin, its should be ok
2: put one wheel on the sidewalk and one in the grass/mud, again warm up your car and do a burn out, if you can leave a black mark on the sidewalk, your lsd should be fine
3: wait till dry and do a burn out after warming up your car, then burn out and if you can leave 2 black streaks, your lsd should be fine.
try changing out your diff fluid and when you drain it, look for metal stuff that falls out, if there is stuff that falls out, your screwed (sorry)
check this out for further help, http://www.mazdatrix.com/g2.htm
I'll try to look for more stuff for you later. Good luck
P.S. what do you mean by "there seem to be a lot of play in the diff when changing direction. "