What's the best way to go about the business side of the production of a feature film ... to use a business that already exists (i.e. my production company) or create a new LLC or S-Corp specifically for that particular production, with the assumption the business will go away once the production is over? (I know the Rolling Stones form a new C-Corp for every tour, that then gets disolved once it's over).

I don't know anything about this, but why go through the hassle? Most people
here have on production company that does all the work, I think.

If you are going to get investors, then form a seperate LLC. You don't want people owning a piece of your ProCo.

separate company for the feature .. depending on how many investors you have NOW and how many you plan will determine if you go LLC or S Corp ..