I used the free Amazon app ES FileMgr to browse and select a sideloaded movie and played the .mp4 movie for a few minutes on the stock movie player app. It worked great, just beautiful. I paused the movie, went to the HOME screen and did something else. When I next opened ESFM, the movie started playing. I couldn't actually figure out how to stop it and had to delete the movie in order to use ESFM to look at other folders and files.
I opened books selected by ESFM in a similar manner and it worked as expected, without this problem.
I am probably doing something wrong? Perhaps I need to stop the movie player app explicitly? How is this done?