Miss fires. jerks when de-accelerating. idle increases then decreases

If you would like help we would need the DTC - diagnostic trouble code .Is their a Reduced Engine Power Mode message showing on the instrument cluster ?
Reduced Engine Power Mode
When the PCM detects a problem with the throttle actuator control (TAC) system the PCM enters one of the following Reduced Engine Power Modes:
• Acceleration Limiting--The control module will continue to use the accelerator pedal for throttle control, however the vehicle acceleration is limited.
• Limited Throttle Mode--The control module will continue to use the accelerator pedal for throttle control, however the maximum throttle opening is limited.
• Throttle Default Mode--The control module will turn off the throttle actuator.
• Forced Idle Mode--The control module will perform the following actions:
- Limit engine speed to idle by positioning throttle position, or by controlling fuel and spark if throttle is turned off.
- Ignore accelerator pedal input.
• Engine Shutdown Mode--The control module will disable fuel and de-energize the throttle actuator.
IF you do not know this your best bet would be to take to a qualified repair shop .
DTC P0506
DTC P0507
The throttle actuator control (TAC) motor is controlled by the powertrain control module (PCM). The DC motor located in the throttle body drives the throttle plate. In order to decrease idle speed, the PCM commands the throttle closed reducing air flow into the engine and the idle speed decreases. In order to increase idle speed, the PCM commands the throttle plate open allowing more air to pass the throttle plate. If the actual idle RPM does not match the desired idle RPM within a calibrated time, this DTC sets.

If the car engine functions without jerks when static and idling responding to increased fuel delivery when accelerator is pressed there is nothing wrong with fuel system. Now while running if it jerks it may be due to breaks in fuel flow, make 7 break in electrical output to the spark plug through capacitor/contract breaker (in earlier models ) or electronics system in MPI systems. There may be another reason --jamming of break due to ma-functioning hydraulic break system. Try elimination defects one by one or take help from a mechanic nearby.

unplug the cruise control

A blinking check engine light is the warning of an engine misfire that can cause damage to the catalytic converter. Check car by diagnostic tool and keep car well.

They come with a 3 or 4 cyl engine, but either way it would not take much to make it run rough.
Usually a miss-fire under load is ignition related.
Have you checked or replaced the plugs, cap, rotor, and wires ?
If not I would start with an inspection of that first.

here are the converter symtoms: decreased low rpm power, engine runs a little hotter then normal at cruising speed, exhaust leaks near header, bucking or jerking during accelerating, cats exterior surface temp cooler near outlet. if you suspect the cat of being bad take it to a garage, to find out for sure if it is, have a good day !!

Ford 2004 6.0, Driving down road seams like when it starts warming up it starts Missing or accelerating,jerking,as long as you keep the acceleration it seems to work as soon as you level it out it starts missing,even dies at stoping sometimes...Changed fuel filter, put fuel additive in tank still missing,HELP

Sounds like you have a leaking cylinder head gasket

Im having the same issue I believe. I have a 94\' Chevy 1500 and when i accelerate it will jerk like the gas has cut out but it wont stall. It just jerks and slows me down. It only seems to do it when going up a hill. I feel like it could be the fuel pump or possibly some intake gaskets?