Copyright issue applies to all services that allow you to save a page, even Google would be guilty for caching. It is up to the user to judge for a copyright infringement before saving a page.
How do you guard yourself against user-shared copyrighted content* ? Do you delete on request from the copyright holders? Do you weed out in the shared content once in a while? Do you have some kind of policy or agreement transfering the infrigement to the sharing user in such cases ?
*Say, a user has access to some content behind a paywall, but shares it un-blocked through your service.