Before jumping in to serving "other media" I think it should be important if not imperitive to clearly define the definition of the term, and not just give examples of what it could be used for.
- What is "other media" in this context? Just ebooks and music, or more? Pictures? Videos? Movies?
- What is the purpose of the media, and how will it enrich the F-Droid project?
- How will the vetting process be applied? Similar to apps, but how? What other steps will be taken, and will this cause concern with potential content creators?
Legal implications can arise from the most backwards circumstances, like @frief pointed out. What types of media are handled will be a significant instigator in the possibility of any future issues. An official F-Droid repo for serving this media will also paint the brand as more than just apps, which from the current results of the poll there are some that don't want that.
There are also the chances, of course, that media licensed under a free license and deemed fit for the repo, could end up being a derivative or infringing work, and situations such as this are often a much larger issue than with code and apps. Even with the best intentions put forward, chances for conflict should be expected.
It should also be noted that there could be a large influx of media to be put in the repository, whichever it may be for that purpose. A new way of submitting content for inclusion may be required if this is the case, to help mitigate stress on those allowing it.
Like @frief stated, using a pre-existing media service such as Wikimedia would not only help shift the blame away from F-Droid in the face of crisis (as mean as that sounds, it is something to consider), but it would also immediately open up lots of relevant media for inclusion, rather than requiring the repository to be populated from the ground up. Not sure how any of that would work out though.
As long as the media served is wholesome to the free software community in some way, and continues to uphold good licensing practices, the only other major problem to arise is a disgruntled fanbase that believes F-Droid should be only about apps, and nothing else. Putting the media in a separate repository would let people choose what they want to see and what they don't, at least. I support media, but only in it's own repository, and when applied to a more strict process for inclusion.
If media such as stock photos, sounds, and other things are included in F-Droid repositories, it may also be beneficial to focus on desktop access to help widen the scope of the project and the number of people it reaches. Surely there would be those interested in using the resources of the project on a desktop if it were to serve more than just apps?
Disclaimer: First post; I'm not much into the politics of F-Droid, or if there even really are any, so please excuse any ignorance