Yesterday stackexchange (or at least part of it) was (briefly) in read-only mode, during that time on the website there was a banner indicating that the site was in read only mode. However withing the iOS app there was no such indication, worse if you tried to take some action (I only tried voting, but I'm assuming other actions would have been the same) it would fail without saying why.
The best indicator would be one that would say, upon attempting an action that would require write access:
The site is currently in read-only mode. You may still take this action, but it will be queued and performed later, and not immediately.
Thus allowing one to continue to vote, compose answers, questions, and comments.
But, of course, this will take more work than a simple, "The site is currently in read-only mode. Please try again later, or visit [someurl] for additional information."