I think the only thing I'd like to be improved is just the editor/posting comments/posting entries that feel very outdated. Something slick Wordpress would be incredibly great.
I much prefer this type of community over Tumblr, or even Twitter. Reblogs and Retweets and they're so very fast-paced. I'm too old to have the necessary energy and time to keep up with them, I'm no spring chicken anymore. I'm glad to see you have image hosting, I didn't know! :O
Also, about your app issues? You do know you can make an app and just post it to download on your site. It doesn't have to be available through app store or itunes for us to install them. It's ideal for the lazier and less tech savvy, but it's incredibly easy to allow third party apps to be installed. Just food for thought.
Thank you for being committed to free speech just like Archive of Our Own is, ya'll are gems <3