As you can see in the picture, the upper engine mount on my car is not sitting where it should be. I'm guessing that this is being caused by another mount being worn out, but can only really see the lower right one (and it looks ok). Any suggestions which mount I should be inspecting/replacing?

 

That one, it is loose. Also, how is the other mount sitting? You can see several pics of mounts here:
Motor mount, right side, Volvo S70, replacement instructions

 

When I bought mine it had the upper mount pounded out like that too. You can take it apart and try to use a "C" clamp to press it back in or purchase a stock replacement and press it in. Take your time and be careful as the brace can be bent if you just try to hammer it back in. Or, you can go the easy way and replace it with a polyurethane one. Some people swear by them, others swear at them. IPD is one source and for $26 it's worth not having the aggravation of it coming out again. I've had mine for over a year and haven't noticed any additional vibration but that is the complaint some people have against them.
The polyurethane is harder so it is more likely to transmit a bit more engine vibration to the body. My personal opinion is if you're getting a noticeable vibration from it either you didn't follow the instructions on how to install it or you may have another mount going out. Third choice is you have a very sensitive butt

 

I second the ipd mount. Been running that for close to two years now and have zero complaints. I also put in the ipd transmission mount.

 

Thanks very much for the input. I have been looking at the poly mounts for a while now, and thinking that this is the perfect opportunity to start replacing them I ordered one from IPD along with a lower right mount. The car has 210k kms and looking through the repair history there is no indication that any of them have been done. Even though the lower right mount looks to be OK its probably just a matter of time till it implodes. I have a hard time believing that the vibration with new mounts will be worse than the vibration I am getting now accelerating from a standstill in 1st. I'll probably replace the transmission thrust mount and the firewall bushing with poly ones in the near future as well, just a little short on $ atmo.

 

On the front engine mount, it may be worn but not blown. If you look at the end of the mount you can see the slot in it. There is a pin that stops it from lifting out of the mount in the event it's torn. When the mount is installed, that pin should be in the middle of the slot. If the pin is in the bottom of the mount it's worn out or torn and needs to be replaced.

I installed the transmission torque poly mount on a T-5R and our S70, you will feel the vibration at low speeds. My current wagon does NOT have any of the poly mounts installed and I have no vibration. So, the poly mount may cause your car to have the same vibration that you currently have. I like the mounts because they are so durable and will likely outlast the car at this point.

 

Question: With respect to the lower right side engine mount--Is there any evidence that this could, if faulty, could lead to shifting issues with an auto? I know I am just grasping for straws here but you never know.

 

I don't think so.

 

I expected as much but I had to ask. Thanks RSPI

 

if all your mounts are blown out and I mean blown out and the motor bangs back and forth you will get shift shock, very common on lexus' and toyota v6's but ive only seen it happen on a volvo once. if your having shifting issues too id do a trans service and clean your pnp switch and see if it helps