What are the copyright laws and intellectual property issues associated with an app like Pocket that you can save articles to read later from around the web?

There are usually very carefully drafted provisions (eg transient copies still allowable until the TPP is enacted) and if the apps are smart enough, they may only keep a link, metadata or cached copy to implement viewings/performance rights which is usually the limits of what the originator intends. You have to realise that copyright is a balance between artists and the public so fair use/dealings applies and so long as the original rights are not infringed, usually no revenue for complaint. I suspect the exemption applied in this case is time/space shifting which is permissible.

Pocket is a general purpose website. As such, it only makes copies at the direction of users. Such automated copies have been held by the courts to be "non-volitional," and thus not infringing. (see, e.g. the famous Religious Technology Center v. Netcom case).

However, liability doesn't end there. Pocket could be liable for secondary infringement, but materially aiding others - it's users - to copy and display articles. This would be, in fact, infringement. But that's not the end of the story.

First, users picking stories to save and retrieve later may well be considered fair use. And it's not infringement to help people "fairly use" copyrighted material.

Second, Pocket and others likely follow the Digital Millennium Copyright Act and are thus protected by its safe harbors. That law says that information providers are immune for infringement relating to storing the content of others, so long as they remove such content when requested by the copyright holder. It's the same law that allows YouTube, Google, and a million other websites to exist. Someone unhappy that a user has saved a copyrighted article can send a request, and Pocket would have to take it down. The user would then have to argue that the saving was fair use.

So, the answer is that Pocket likely is aiding some infringement, but not to the extent that news people are sending takedown notices. Given that Pocket has a lot of sponsored content, it is likely that they have permission for a lot of content as well.