I have always thought it should be copyright issues instead of copyrights issues, and Google search results also support that copyright issues is much more common. I thought it was simple, as attributive nouns should take the singular. But I have also found a number of instances of copyrights issues likely written by native speakers:
In U.S. may be copyrights issues and contracts; in EU must deal with special database protection. (by an American lawyer)
Therefore, it’s not surprising to see industries that deal with copyrights issues first hand jumping in on the possible opportunity and trying to develop projects that will make that a reality.
The good news though, is government bodies are actively looking for ways to sort out the copyrights issues brought up by social media. (from here)
Also if it is copyright issues, why is it movie rights issues? Shouldn't the attributive noun be in the singular? Is there consistency in these terms? Some examples I have seen:
Cuban Link indicated that he may no longer be involved with the project as the result of movie rights issues and creative control. (from here)
Unfortunately, each of these projects fizzled out due to rights issues regarding the music or just because of other career obligations. (from here)
But even more helpful have been the diagrams detailing the complicated rights issues surrounding Marvel Comics characters, their varying cinematic universes, and studios. Following Disney buying 20th Century Fox (which, yes, hasn’t been officially allowed yet), the rights issue became much clearer, but still not cut and dry in some areas, as this updated infographic shows. (from here)