Do you reference the executive producers for a motion picture along with the producers?
In discussing the citation of motion pictures, APA places the greatest emphasis on the producers and the director, treating them similar to the author of a book or article. As to the executive producers, I would say they are optional but certainly not mandatory. Generally speaking, APA is flexible and allows you to add extra information to a reference for the sake of clarity; it's just important to format everything correctly and ensure the essential elements are present. For some films there are quite a number of producers and executive producers, so there wouldn't really be space to list them all anyway (you only list up to 7 authors per APA style).
For Dangerous Minds, it looks like there are 2 producers and 3 executive producers, so you could list all five if you'd like to. I would separate them into two groups, putting the producers first and then the executive producers, followed by the director. However, since the executive producers are not essential, it may be easier just to leave them out.