I am not a lawyer. The following is based on what I've been able to gather.
For specific legal advice, particularly advice corresponding to whatever jurisdiction you operate the server in, consult an intellectual property attorney licensed to practice within that jurisdiction.
With respect to simply operating a server with content that belongs to you, whose content is available only internal to your LAN, that's your business.
With respect to whether or not your broadband provider's AUP/TOS permits you to host a publicly available server that's specific to your broadband provider, read the AUP/TOS before deciding whether to do it or not.
if it's your own content, there shouldn't be any problem, though if you make it publicly available, you might want to consider making it available subject to the terms of a Creative Commons License.
As for serving up content created by other people, make sure you have their written permission on file. With respect to making commercially recorded content publicly available via a media server, I do not do this or recommend itthis guarantees problems with the *AA organizations.