Bad Engine Mounts?? Help Diagnose

When I first start the car, and the car is in park, everything is fine. No vibrations and Idles just perfectly. Whenever I hold the brakes and put the car in reverse my car starts to shake and continues to shake. I notice the RPM's will drop 2-300 for about two seconds, then go back to normal. Once im driving its perfect, no vibrations or anything. When I stop at stop lights the car rattles slightly, and I also notice once I turn the A/C or Heat on, it will Shake also. Im guessing bad mounts? But I could use some help on this. And at the stop lights also, I will put it in Neutral to stop the shaking.