When you are working under your vehicle, make sure it is supported by secure jack stands. There is always accident reports indicating someone has been injured because due to working under a car that was only supported by the jack. Please do not take any chances.
Changing the differential fluid is valued at approximately a $135 for the service and fluids. It really doesn't take that long, nor is it that difficult. The procedure just seems a bit daunting when you first think about doing the work on your own.
The subject vehicle for this procedure is a 2002 GT. You will require a 3/8 drive socket set, a slot screw driver, a scraper tool and some high temperature silicone and a drain pan. The fluid required is 2 quarts/litres of differential fluid and 2 bottles of Friction Modifier. The differential is a limited slip configuration and the clutches require the addition of the friction modifier. People who leave out the friction modifier will start to generate excessive rear end noise and will have to add it anyway.
Start by putting the car up on a lift or jacking the car up as high as possible and supporting it with jack stands. Do not, absolutely do not attempt this procedure with the vehicle supported only by the lifting jack.
Once you have the vehicle securely supported by jack stands, start by loosening all the bolts that surround the rear differential pan. There will be a aluminum tag attached to one or more of the bolts that specify the gear configuration of you vehicle unless you have changed the gear ratio. If you have these, don't loose them, we will replace them during re-assembly. Once you have removed all the bolts, slow pry the pan away from the differential housing near the bottom, being careful to not damage the pan. You will need just enough prying force to break the silicone seal between the two mating surfaces. Once you have broken the seal just enough for the fluid to start running, let it run. This is nasty smelling stuff and you don't want to get any on your clothing.
Once you have drained the differential completely, continue to pry the pan away until it is free. Remove it completely by lifting it up over the rear sway bar. Use the scraper to remove all the excess silicone sealant from the mating edge of the pan, and clean any fluid gunk from the pan itself.
Re-direct your attention to the mating surface of the differential housing and clean it with the scraper as well. There is always some differential fluid that does not drain out completely. Take some throw away rags or paper towel and clean the bottom of the housing. Once complete, clean clean the mating housing surface again with some solvent so that it is clean and dry.
The pan will now need to have the high temperature silicone applied to it before closing up the differential. It is easier to apply this to the pan than to the vertical surface of the housing. Carefully maneuver the pan back into position being careful not to touch the silicone surface to anything. Any contamination could be a source for a leaky rear end. Replace a the bolts with any tabs and finger tighten as much as possible. With your socket, slowly tighten each bolt using a criss-cross pattern. This will ensure a good flat mating surface between the pan and the housing.
If time permits, it is best to leave the pan for several hours or over night to allow the silicone to cure completely. This really diminishes the possibility of leaks.
When the minimum time specified has elapsed, a socket driver with an extension will be required to remove the filler plug on the front side of the differential. This is on the drivers side, just above half way. Cut the end off of the spout provided on the differential fluid and empty 2 quarts/litres into the differential. Now add the 2 bottle of friction modifier and the housing should be full. If it does not already start running out, you should at least be able to stick you finger into the hole, and touch the fluid, this is adequate. If not, you may have to add a portion of another quart/litre of differential fluid.
Replace the plug and tighten. Over tightening can strip the thread and lead to a cost repair and a pile of wasted fluid. I had the transmission in neutral, which allowed me to turn the drive shaft a couple of revolutions, making sure the gear surfaces where covered and to help mix the fluid and the friction modifier. Check all you bolts and plugs are secure, slowly let the car down off the jack stands and you are finished.