my diff started leaking at around 7,000 miles. just buy the silicon from the dealership (don't forget to buy the limited slip additive and gear oil while your there). take off the cover yourself then scrape off the old silicon using a razor blade. then set the cover on a flat surface and check to see that are no spots where it bends up. then what you want to do if scrape the old silicon off the diff. itself. clean everything really well and apply the silicon (use a lot, but not all of it) to the cover. then bolt on the cover to the diff. try to use a sequence like that of tightening a tire. don't forget to add that limited slip additive.
i did this myself because i didn't want the dealership to add any "hard" miles to my car. dealership porters know what i'm talking about.
my 2001 gt now has 35,000 miles on it without a leak.
whhooops i didn't see the last two posts, but go down there and check. it's most likely the differential cover. it's easier than you might think.