It is a 2005 Saturn ION that has about 141,000 miles on it.
Received a code P0302 from a scanner loaned to me. Did a rescan and the code did not appear again.
That's a code for a Cylinder #2 misfire.
The fact that the light hasn't come back just means that the misfire is transient. Chances are that in a couple hundred miles the light will come back.
If you've never changed the spark plugs, start with that.
ZV
The Check Engine light was flashing on acceleration
Would that cause the front transmission mount to rock?
Per every revolution of the crankshaft, your engine fires two cylinders.
If you have a dead miss on one, that means on every other crank revolution, there's going to be a big awkward hole. It's not going to be pleasant, and yes, it will result in very rough and vibration-heavy operation.
You may want to take this to someone. You're going to end up trashing your catalytic converter(s) and possibly your engine over a problem that can probably be fixed for well under a hundred bucks in parts.
200 bucks at an honest mechanic will fix it