Whilst playing the App over the weekend (love it!), we ran into an App rules question. We hit the information/help/rules button (whatever it's called) which took us to the pdf on the SW:IA main site. We looked for an answer and returned to the game. The App reset. Now, once we loaded our save, our progress was back to the correct mission and round (yay!). However, it was top of round where we had been multiple activations in (oh no!). We marked CAHRACTER-ONE has having gone, then it activated a random unit which hadn't previously activated. We were able to adjust, for the most part, but because the Imperial activation block isn't available for recall, we had to improvise how the new enemies attacked when we got back to our game state.
Now, knowing how this happens, we would be prepared to memorize the enemies' attack blocks next time. We could have tried to undo all damage and movement and actions that round (to the best of our memories), but because we'd rolled poorly, we felt as though it would be cheating.
In Mansions of Madness 2, when the App saves, I believe it does so between phases, which are particularly easy to recreate.
I am also ecstatic to find that it saves at least between rounds.
I don't know that this is particularly a bug, but it is something to be mindful of as both players and programmers. I get why it would take you to the website (although that does add internet dependency) to see the rules: it reduces the number of places the rules need to be updated.