This is the part which blocks it for me[1] - although I will give them credit for being upfront and honest about it when you launch the app the first time.
[1] if they release a phone-local version, however limited, I'll definitely give that a proper go to see how good their tech is.
> All photos reviewed and organized via the App will only be saved temporarily on servers for the duration of the review process. The photos will be deleted immediately upon completion of such process. We will not make your photos available to others and we will not store them. No human will ever see your photos during the review process.
http://roll.eyeem.com/privacy.html
Also note that we are a German company, so German privacy laws apply.