RE: F150 ENGINE RUNNING ROUGH
In most cases of running rough on the 4.6 and 5.4 a bad coil will give you those symptoms. When it's idling rough, unplug each of the ignition coils 1 by 1 and take note of the one that makes the least difference in idle. When you've found the misfiring cylinder, pull the coil and check the boot for signs of water contamination. Most commonly, #4 cylinder will have water/coolant contamination due to the heater hose connection above it leaking.
If the coil boot and spark plug hole is dry, swap that coil with one next to it and re-do the test I mentioned above. If it's the coil, the misfire will transfer over to the other cylinder.