My car was idling rough (like the way you're describing it, dropping it into neutral while cruising to a stop, etc.)...I was also having hard start issues. Found out that my positive connection on my battery terminal was really loose. Apparently, whoever the last monkey working on my car was, left the fucking thing loose.
It was so loose that it was almost off. This was causing my car to run rough at times, and cause my hard start issues, cause the freaking voltage was literally having to jump from one connection to another. Needless to say, the top part of the battery plastic, (where the positive wiring lays on the battery) was actually melted through some.
I basically tightened down the connection and the car runs much smoother now, and no more hard start issues.