Engine mount is pretty easy to check. Have someone put the car in first, stomp on the brakes (+ handbrake, don't want your ass getting run over) and let out the clutch while giving the car a touch of throttle. Watch for excessive engine movement. If the engine pitches up and forward, check the rear mount. If it pitches downward, watch the front mount. It's pretty obvious if the front is toast.

Checking the axles is pretty easy too. Just get the car in the air and look for cracks or chunks missing from the axle boots. If the boots are solid, grab the axles themselves and see if they move around. A bad joint will usually shift around pretty easily.