So attempting to (yet again) track down the cause of a clunk in the front, the mechanic shoves a pry bar under the engine and effortlessly lifts the whole thing up a good 3 or so inches and shows me that the 2 engine mounts have a gap in them when he does this - this is new territory for me, he says that indicates the motor mounts are shot - is that true? If so, what happens from worn out motor mounts?

He also pointed out the rubber on the transmission mount is split on one of the branches (the pieces separate when the transmission is wedged upward.)

The clunk happens over bumps and can be easily replicated by rapidly steering side-to-side while driving (at parking-lot speeds.) Other than the noise, the car seems to handle and steer very well, and tracks perfectly straight.

 

The motor moves around more than it's supposed to and this can damage things that go from the motor to fixed chassis points (hoses, connectors, etc). More noise/vibration transmission from engine to chassis. Increased movement under acceleration and engine braking, and in severe cases while turning hard.

You can see this by opening the hood and shifting into reverse or drive, then WHILE CONTINUING TO HOLD THE BRAKE DOWN gently rev the engine and watch the engine assembly for movement. With good motor mounts it shouldn't move much. This is one of those times the forward folding hood makes life a bit easier. On our cars, the engine will rock left or right depending if you select drive or reverse, try both to test each side.

 

Definitely get both engine mounts and transmission mount replaced ASAP.. That's how I got my 98' XJR from the previous owner. The mounts were so sagged and separated that the transmission oil cooler tube had a hole rubbed thru from resting on the subframe. It leaked a lot of oil out and the transmission started acting weird. Let me put it to you this way, if you replaced all 3 mounts and it still didn't solve your noise over bumps, then it's still money well spent because he showed you how much your engine moved. Your air intake tube will also get a trot of excessive movement as well as what Nilanium said, your hoses connected to plastic start to strain.

 

Thanks - what is the likelihood that the failed motor mounts are causing the clunk?

 

Please get the mounts fixed asap as stated below. This can be fatal to your car if it's not fixed.

There are about a hundred things that can happen with the car in this condition. Most of them are really bad.

Mounts are not expensive.(Maybe 200 bucks tops for the engine mount pair and another 50 for the tranny mount). It's not difficult to change them. They are bolt on's.
I suggest changing the nuts and bolts that anchor the mounts to the frame and engine too as these bolts are major stress points.

As stated before, even if this does not solve your issue, you are avoiding killing your car because of broken mounts.