1998 Saturn SL2, 1.9 Twin Cam
Car shakes alot at idle, driving down highway no shaking. What is wrong? Any common problems with these cars? Possible motor mounts? if so how do you check them?

Vehicle runs ok, just replaced fuel filter and spark plugs, car over heated a year ago, vehicle has new cylinder head and Radiator. Shakes and trembles when idling at 1200 Rpms, when starting cold, When idling at 888 Rpms the desired idle speed for this car it does not shake.

Could be a combination of things causing an engine misfire. But first I'd replace the spark plug wires (if so equipped). Also add some Chevron Techron concentrated fuel additive to the fuel tank. You could try some CRC also to clean carbon from the engine.
http://www.chevron.com/products/prodserv/fuels/additives/concentrate_plus.shtml
http://www.crcindustries.com/auto/content/prod_detail.aspx?PN=05063%2D6&S=N

Motor mounts - dog bones

Both need replacing - they are known for failure.

And you described the symptoms perfectly.

The top engine mount, located next to the valve cover on the left side of the engine, is prone to collapsing over time. Replace it. I'd recommend bucking up for the Saturn part, as the aftermarket ones don't tend to last very long.