My question about using the brake was related to a transmission issue where the torque converter may be unlocked when the brake is applied. So that may not be relevant now.
So the apparent misfire occurs mainly on deceleration and can occur on moving off from rest. What about your idle? Is it smooth in park and when drive engaged? Engine speed is controlled by an electronic throttle system and does not use a throttle cable so changing engine loads are accommodated more quickly than with the old IAC systems. Do you notice any slowness in changing idle speed to cope with A/C loads etc?
Misfires are generally caused by failing spark plugs, how many miles since they were changed? Usually a code will be set for a misfire that lasts for any length of time i.e. P0300 for multiple cylinders or P030x where x is the misfiring cylinder. You can do the following checks:
1. remove the coil on plug (COP) by disconnecting the electrical connector and then removing the hold down screw using a 7 mm hex socket and twist the COP out of the plug well;
2. look for moisture in the plug well and see if it is coolant or just water;
3. look for dark streaks down the porcelain on the plug itself that may show signs of grounding of the spark;
4. check the spark plug rubber boot for signs of deterioration, burnt holes, tears etc. The boot can be replaced without replacing the COP;
5. check the wire connector that fits onto the plug for corrosion;
6. The spark plugs themselves may be failing, but this is a "difficult" job due to a carbon buidup in the lower part of the plug so leave the plug in place until you have learned the procedure.
Another cause for misfires is a vacuum leak where a hose or gasket or component allows excess air into the intake and causes a lean burn misfire. You can check the vacuum in the intake with an inexpensive vacuum gauge. You will need a port, such as the brake booster hose, to plug the gauge into. With the engine idling you need a steady reading of about 18" of Hg or higher. Readings significantly below and flickering indicate a leak. To find the leak use a liquid fuel such as carb cleaner or a specialty CRC product that will not damage the CATs. Spray the fuel at particular areas along the engine looking for the engine speed to increase noticeably. The popular places are the throttle body, intake manifold gaskets, PCV hoses, EVAP hoses, vacuum lines and their connectors, etc.
The EGR can cause poor engine operation by allowing excess exhaust gases into the intake. The EGR should be closed at idle and low speed. I am not sure yet how the Explorer EGR operates since Ford utilizes many different types.
An exhaust leak such as from the manifold can cause poor scavenging of the combustion gasses through the overlap of intake and exhaust valve openings which would be excessive in high vacuum conditions - trailing throttle slow downs. An exhaust leak would be most noticeable at cold start and diminish as the engine warms up. You may be able to hear the ticking sound from a leak or feel the escaping exhaust gasses. Since the engine fan will cause air flow around the manifold this may be a challenge.
Check that the injectors are all working the same. The injectors will make an audible clicking sound, see if all injectors are making the same sound. Put your fingers on each injector in turn to see that the pulse appears similar for each.
Check the air filter is clean, and that it is not oily (K&N type). Oil from K&N filters will get on the MAF sensor and change the electrical resistance causing a false reading of air flow to the PCM.
Check that the MAF electrical connection is in place since it is removed when changing the air filter.
Good luck.
