Those poorly flagged DVD titles are one reason the Faroudja and Silicon Image de-interlacers are popular, they can switch in and out of FILM mode faster and with higher picture quality than the cheaper de-interlacers in the JVC and other under $300 players.
Yes even with some movies, they convert it to video and then edit it there - messing up the 3:2 pulldown sequence, its more common with TV episodes than movies however. Try forcing the JVC mode to FILM and see if you see any combing during those sequences where you know it switches between red...
When the JVC light changes between red and green, it means the DVD title has both film and video-based editted sections, this is common on some sources like TV shows on DVD. If the light glows orange, the title has the alternating progressive flag problem and you should manually select FILM mode...