Try pressing Ctrl-Alt-Shift-T during playback of one of the problematic videos. It toggles between the different deinterlacing methods, so try all the settings (video, film, auto, off) and see if any one of them works. Some video content is shot in 24, but then broadcast at 59, and that content needs "film" type reverse telecine deinterlacing. Conventional 24p content (movies) doesn't require deinterlacing, and conventional broadcast content in 59 works fine with "video" type deinterlacing.
I suspect your content might need "film" type deinterlacing, because (as I recall) "auto" defaults to "video" when it can't figure things out. If you find a mode that works, you can set the mode for the files individually if there are only a few, or if you want to do a bunch use jriver's rename utility to add deint=film to the end of the file name (but before the file extension), and JRiver will handle them correctly.