I believe that I have either a bad transmission mount or mounts, and possible a bad motor mount or mounts because the car vibrates in drive while running and also vibrates in neutral while running but not nearly as bad in neutral. How can I tell by looking at the mounts which ones are bad and which ones are good ?

Get a friend to open the hood and look at the engine go up or down in the engine compartment when the brakes are firmly applied and switching between reverse and drive. Look for the motor mounts for behavior where tears exist in the rubber.

Hard (from age and heat) or broken engine and transmission mounts will cause this type of vibration. Based on many repair experiences with this type of vibration on mostly 4 cylinders I would replace all the mounts, both the engine and transmission, leave the bolts loose that retain the engine in the mounts, then with the motor mounts and transmission mount still loose run the engine and shift back and forth from drive to reverse and then back to neutral, this relieves any stress from misaligned engine mounts and reduces vibration. Also make sure the exhaust isn't touching the frame anywhere, that will also cause vibration to be felt at or near idle, worse when put in gear. If all of the above don't help then you may have a torque converter problem is it is an automatic transmission

Bad transmission mount will give constant vibrations on the road.very annoying. Often, bad motor mounts allow the engine to rock and move around, causing noise and interference problems with the throttle, transmission and clutch linkages. For example, a thumping noise when the transmission is put into gear or when the vehicle is accelerating is a classic symptom of a bad mount. also when climbing hills it will jump around. from the strain going up hill, that is putting torque on the engine. good-day ! on most vehicles you can start the vehicle, then put foot on brake. have someone watch engine when putting torque on it. if the mounts are bad. you will see engine move or bad vibration.