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.