That is shadetree as hell. The engine can detect misfires and not throw a CEL. It will store a code. It has to have so many misfires per revolution to throw a code but it still detects and stores them if the number doesn't pass the threshold.
Did not know that. In that case, take it to a good machanic and put a computer on it. Replacing them is pretty straight forward. Don't buy the cheap chinese coils. Get the factory ones. They run around 50-150 bucks depending on where you buy them from and most mechanics charge 100-200 in labor to replace them because they are a pain in the ass to get to. http://www.amazon.com/Motorcraft-DG...&ie=UTF8&qid=1407300362&sr=1-4&keywords=DG511
Do the vibrations decrease or go away when you rev the engine at high RPMs? I will be the 18th guy on this thread to say its probably the coils. I had an 02 F-150 with a 5.4L and mine started going out at around 90k. People will say once one goes bad you might as well replace them all because they will start failing at around the same time. I did not find this to be true for my truck. My cheap code reader had the codes and stated which coil was the problem.
If the vibrations go away while moving probably motor mounts. If it keeps vibrating while moving probably coils or something is loose.
Ford did a survey and 2/3 of the coils that their own techs replaced were found to have no issues at all. Coils are not always at fault. Any number of problems can cause a misfire in a particular cylinder and that is assuming this car even has a misfire. The coils also have rubber boots that when they crack can cause problems but the coil is fine. These boots cost about 3 dollars. Replacing all the coils is just a bad advice.
I wasn't recommending for him to change all of the coils. I was actually saying that I was told to replace them all when I only had 1 out of 8 that ever failed. I had misfires caused by both a failed coil pack and a fuel injector seal. If it is a misfire then it should hopefully show up an a code scan and OP can go from there.
There isn't any labor savings by doing that and they are not a wear item (like tires, spark plug) so that is also some bad advice you got.