To check for engine mount failure try the following;
Get a friend, Pop the hood, start the car and have your friend put the car into reverse, then drive at idle. The engine will move, but not significantly... unless the mounts have failed.
With the passenger side mount, look for an oil stain on the frame rail right next to the mount.
For the front and rear mounts, there is a vacuum line attached to a small black box (solenoid valve) on the left suspension mound. With a tool like a mighty vac, try and pull a vacuum on the line. No vacuum = failure.
LINK to some pictures showing testing of each mount individually to find the culprit.
The transmission mounts can be seen thru the left wheel bay. Turn the wheel or jack up the car and remove the wheel. 2 small mounts, there are probably torn off.
Fixing the rear mount is a pain.
LINK to me installing the rear mount and a show and tell on how the mount works - it's not just rubber.