We have implemented a GoogleReader-like mobile API that allows anyone to create a mobile app that works with The Old Reader. The API is documented in a separate github repository. Please drop us a note if you create an app that works with The Old Reader.
Please note that apps require you to have a username and password in The Old Reader. If you currently only use Google or Facebook to sign in, you will need to create a username and password in settings.
There are a number of browser extensions that make tracking your unread items easier.