The engine was misfiring for quite a while. At some point, the battery went dead due to a bad alternator and all the electrical systems went nuts. I replaced the alternator & battery. At some point, I got a po303 diag. code. I changed plugs & wires the code went away. The misfiring seemed to go away. A day or 2 later the po303 code returned after a 100 mile drive. I pulled #3 plug & wire & reinstalled them. The code went away. It seemed to run better for a while. Then it started misfiring again. A few days later, it showed a po420 code. A few days later while researching for a repair to fix the po420 code, the code disappeared. A few days later It got a po306 code. Misfires in #3 then in #6 suggested a bad coil tower & I replaced it. It seemed to run great. A day or so later, it started to misfire again. At this point the misfire seems worse after first starting the vehicle. At one point today, when we sat at a traffic light in gear it missed. Putting it in neutral or parks, cleared the misfire. After parking for 30 minutes, it misfires both in gear or out of gear. Any suggestions would be helpful.
Sounds like a bad ECM (engine control module, AKA the computer). Its a common issue with your vehicle.
A bad ECM will throw inconsistent error codes. Have a mechanic test with another ECM before you set off and replace other items.
Sounds like an electrical leakage. If the cables will reach, put cables 3+6 on 1,2,4 or 5 and see if the misfire persists on 3/6. if it does, check the coils.
The p0420 code refers to a low catalyst threshold. If your misfire isn't due to a leakage, you might have a bad catalytic converter.
Since multiple parts were already replaced I'd be looking at the signal from the crank sensor to the PCM (brown/light blue). As well as signal from PCM to coil 3 (brown/orange) 5v square wave. IIRC coil 3 is the 3/6 pack, this should be a 12v square wave.
Don't forget about the fuel system either. You should test fuel pressure and injector signal/injector function.
You should also make sure the engine is mechanically sound, do a compression test, check engine vacuum etc...