Transmission Diagnostic Prob?

I have a 2000 Ford Crown Victoria. I bought this car because of their superb reviews for durability and lack of repair costs… However mine, which I just bought, now decided to give me transmission problems. When I shift into reverse when first starting the car, it does a hard shift. But if I'm driving, stop and then shift into reverse, it doesn't seem to do it. Also, while accelerating quickly as if I'm getting onto the interstate, the shift from 2nd to 3rd is a hard shift also. I have looked up possible problems and I see too much to take in. I'm hoping my specific problem can be answered in one place. If you have any questions that would help lead to an answer, feel free to ask and I will post an update as soon as possible.

I can think of at least six things that could cause this, none of them DIY fixes. Get it to a transmission shop and have it professionally diagnosed.

The tranny is 14 years old, you don't give a mileage. There could be a transmission or engine mount problem, or a bad torque converter, i would bet a paycheck that there's a Crown Vic owner's forum you could join and ask the question there.
Oh look, http://www.crownvic.net/ubbthreads/ubbthreads.php

Not enuff info for us to guess… But dittos to the response that it's 14 years old. Those cars are known for running-up 300,000 miles over just a couple years in fleet use. But time takes a toll as well. And… You probably don't have the service history for 14 years: was the transmission serviced as Ford recommends, which probably includes a lot of fluid and filter changes, that may or may not have been done.

I had a Mercury Grand Marquis, about the same year and they are basically the same car. My transmission was chattering when I was driving. I had the transmission fluid replaced and shortly thereafter the problem stopped. As far as I can tell those cars need new transmission fluid every so often. I would go to a place like Precision Tune, where they have a machine that will swap out your fluid. It will cost around $100 but it is well worth it. You may want to have the transmission filter changed also.