There are "Fair Use" copyright laws, though they are hazy, that say it may be okay to have other copyrighted works within your video to some degree.
But anyway, I'm not concerned, because this video is only intended for the internet (there aren't really any better venues outside of the internet for music videos anyway), and they're not particularly recognizable clips for anyone except for super movie nerds. Whoever owns the rights to those films would doubtfully ever see this, or be hurt by this, or even if they did see it, they wouldn't be litigious about it. And even if I used a clip from a major movie, and the studio found out, they'd almost definitely just ask me to take it down (cease and desist).
For what I'm doing, and for what those movies are and how they're used, I'm not worried about it.