I would check the spark plug(s)..... If you replace, make sure to use double platinum plugs....as in both the center and ground electrodes being platinum enhanced. Last I knew, only Motorcraft and Autolite brands offered the double platinum.
Cylinder #4 is on the front, passenger side of the engine.
Running a quality fuel system cleaner through on 2 consectitive tanks of gasoline is another thing to try.
If your plug wires are original....you could try replacing them.
If you have not had the EGR ports cleaned.....a missfire on Cylinder #4 or #1 is a common indication of clogged ports. I had a P0304 code that ended up being the EGR ports.....Cylinders #1 and #4 are the farthest from the EGR valve....and seem to be the last ports to become totally clogged.....so they get all the EGR gasses....and thus the misfire. The EGR valve is only open while driving....not at idle.
Another misfire that I had, P0301....Cylinder #1, was caused by crud inside the plastic cup that is over the spray end of the fuel injectors.....I had it on all the injectors, but the problem showed up enough to set a code on cylinder #1 first. I had to remove the fuel injectors....and then just a squirt of carb. cleaner cleared it right up.
I am told that this is common on any high mileage engine (mine is over 145K miles). When the fuel spray first meets the gasses from the PCV and EGR, this buildup happens.
The last 2 items are common, but I would make sure that it is not something easy, like spark plug, or fuel system cleaner first. Also, if the fuel filter has not been changed in a while.....it may be due.
Here is a link to some pictures from my '96 3.8L, On several of the pictures, I have labeled some of the items.
http://community.webshots.com/album/201931518cScpNK
I have discussed some steps to clean the EGR ports and the fuel injectors in a couple of other posts...and the EGR port cleaning has been discussed a lot by people who are more experienced than I am.....