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Hopefully this helps someone because I searched and searched and couldn't come up with an answer to this from anyone on the forums. Most never post an update to a fixed problem. Never understood this but I want to be different, so here goes.
2004 5.4L, 4x4, XLT, Advance Trac with 21,000 miles. Bought it used a few months ago and noticed a vibration at idle when in gear (reverse or any forward gear) while stopped (at a red light stop sign etc.). As soon as you took off, the vibration was gone. It didn't vibrate all the time but did most of the time. If you put it into park or neutral it would immediately stop.
The fix was the dealer calling Ford Hotline and were told to "neutralize the system, take exhaust, lose motor mounts, trans mounts and body mounts, start engine and bring to point of vibration and tighten everything per hotline 041205 9:12 6DLD4007" Concern CD: K03 .
The fix worked and is now smooth as silk in gear while stopped. It was a 5 hour job according to my receipt that was covered under warranty. Hope this helps someone.