Offline Sync
I was using Greader pro for google reader and I was able to download the latest news and read while I was offline. The next time I connects to the net it syncs for rea/unread/liked/starred items...

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Michael Chermside commented
Clearly this would be a MAJOR feature (and thus shouldn't be one of the first items worked on), but a useful one. I think it would be MOST appropriate for text-only content on a mobile or tablet app as there is an obvious place to store the downloaded content as well as a frequent need for disconnected operation.
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Stefan Czerniawski commented
Having an offline store synchronised with an online backend keeps the best features of both. I currently use FeedDemon on pc and NewsRob on android, which keep themselves in step, but have massively better response rates than a purely online service can manage - particularly when on a flaky mobile connection,