2005 Ford Taurus with 3.0 engine. Check engine light keeps coming on. Scanned by garage code showed "cold start cyl. 1 & 3. Car started and ran fine, but changed spark plugs. A few days later, light came on again and code was the same. Replaced all of the coils. Again, the engine started and ran fine even though the light had come on again. A week later, light on again and shows same error code. Service manager @ the dealership suggested taking it somewhere else. They don’t know what to do. Any suggestion?
Which 3.0 engine?
duratec dohc . . . ?!
I’m asking because you said you changed “all of the coils” . . . and the 3.0 Vulcan only has 1 coil pack
When the check engine light is on . . . is it flashing?
Do you know the specific code(s)?
P0300, P0606, PO30X, PO316 are examples of specific codes.
That information would help. Ford has published several Technical Service Bulletins pertaining to your vehicle.
Did they mention anything about re-programming the engine’s control module (computer)?
If the dealer can’t fix it with the car in front of them then most of the folks here will need at least the specific codes to take a guess at the problem since they don’t even have the car.
CSA 
It’s the duratec engine and the light does not flash. It stays on until the technician turns it off when doing the scan.
The last scan showed the following error codes: PO300, 301, 302, 303, 316, & P1270.
Ford DTC P1270 means the engine was operated over it’s rev limit.
This can be caused by racing the vehicle, revving the engine too high in park/neutral, or spinning the tires on ice.
Revving an engine too high can cause valve floating. Which can lead to pistons hitting valves.
Perform compression/leak-down tests to determine if any of the valves are bent.
Tester
Then I’m really concerned about what these error codes are showing. This engine has not seen rpm above roughly 3000 rpm in the 2+ years I’ve had it.
Initially, the cold start error codes didn’t make sense because the engine starts great, runs smooth with no missing, running rough or hesitation.
I don’t understand how an engine can show so many error codes and yet start and run no different than a new one does.