Only a careful inspection will detect loose or deteriorating powertrain mounts. Look for missing chunks of rubber, severe cracking, oil soaking and separation of rubber from the metal on the mounts. Look for loose, broken or missing retaining bolts.
Don't forget to check the dogbone struts on a transverse engine. If they're deteriorated, consider a premium aftermarket replacement that has a hydraulic damper.
Some north-south engines have a mini shock absorber to reduce vibration. To test it, disconnect it at one end, and then compress & extend i. If you feel any lost motion or roughness, it should be replaced. North-south engines also have a mount at the rear for the transmission. A few cars have special vibration dampers, which resemble a stack of rectangular plates, bolted to the transmission. A loose vibration damper doesn't do its job, so make sure the retaining bolts on this assembly are tight.