Shaking around 30-40MPH

Just bought a 98 Crown Vic. So far the cars been great but, since I've had it it seems to shake around 30-40 MPH. I've checked fluids and all seem normal. Worried because I've heard bad things about the trannys in these things. If I accelerate hard you don't notice the shaking at all but when going uphill or slowly accelerating is when you notice it. Could it be a plug or wire gone bad? Sometimes it will do it at a constant from 30 until I hit around 40 and if I brake or let off the gas it goes away so I'm not sure what it is. Car has 130k miles and the usual 4.6l with no upgrades.

Do the tune up first. If that does not cure it, you have what is known as torque converter shudder. You need to exchange ALL the fluid from the transmission, lines and cooler. A transmission flush is the most effective way of doing this. But from your description, I think the tune up will cure the shudder.

Well, I plan on giving it a tune-up soon anyways as well as flush the tranny, change the filter, clean up the magnet, and put lucas and tranny fluid in it. My dad seems to think it might be the rear end giving out but he hasn't taken a ride in it so not sure how much his two-cents counts.

Why Guess? Just take it to a ford dealer, they will use MTS4000 a Vibration analyzer. u will make unnecciesary expences if u start guessing.