For many of us an app-dependent game is just as likely to be a hindrance as a help, so how it's handled is exceptionally important. I really love Mansions and try to ignore it's current flaws, so I'm tentatively excited about a new version. The app seems to me the most crucial, easiest to "break" part of the equation.
Likely the biggest possible issue for an app-dependent property like Mansions, is obsolescence. Just like every pc game you bought in the nineties, eventually the app will no longer be supported, which is fine as long as we have a device that runs the OS the app is native to. But soon, OSes are no longer supported, then the hardware moves on, and the best you can do is get a hardware/os emulator. Not really a solution for the average gamer. This means our game may have a shelf-life tied to the next few generations of hardware (say six years or so). To solve this, I'd suggest that the app speed and supplement play, but that an app-less variant be included in-box - otherwise customers may end up with a box of worthless components.
Someone else has brought up the important problem of app crashes and resuming games. If the game doesn't save often and securely, you could lose a game half way in or near the end. This could make the game unplayable, depending on how often. It's been stated before, but the importance of a solid app with a fully functional 'resume' feature can't be over-stated.
Often times the look of the app is of chief concern, which results in a decent looking app that can be unresponsive, unwieldy or exceptionally slow. In the Arkham Horror app for instance, to flip cards it would often take the app near 2 seconds on some hardware/os pairings. So you'd have to hit the screen twice, then you'd finally get to see the card back and read it. This was much easier to do with the physical cards, because the app took too long for us to use. It may have been fixed in later versions, we just gave on up on it (??) but the point still stands.
Keep in mind also, that though most software engineers design on the fastest hardware, most players will be using older slower platforms, at least eventually. If we're losing up to a second and a half of real life (a non-replenishable resource) for every two player inputs/card flips/whatever because the animation looks cool, is slow, or our hardware/os is slow - the app is getting in the way. If we can't get to the information we need to play instantaneously, it's effectively a *broken* app (which means a broken game in this instance).
Also consider how many touches, swipes, or wait states we have to see to input information, choose a screen element, or begin actual play (not the app). Again, it must be fast fast fast on the oldest hardware, or it doesn't matter how cool it looks (and the "cool" factor wears off by second play-through, so of limited value).
And just as a suggestion I hope at some point players may be able to remove some of the game/gm's powers (sometimes we play with our kids, and remove the hardest spells), or other game elements to speed solo or advanced play. Some suggestions would be, instantaneous combat (no more reading card backs), removing or negating in-game hiding mechanics, skipping puzzles by substituting skill rolls (some players find those elements gimmicky and unnecessary, would rather not pass their hardware around the table to people with gamer hands), removing darkness or fire, etc. Anything that can make repeat play hum through slower parts. A lot of us get relatively short table time as it is.
Although I hope for a fast, lean, bulletproof app, these are my worries, I'd love to hear what you guys think.
Keep in mind for many of us, an app-dependent game is just as likely to be a hindrance as a help, so how it's handled is exceptionally important. Some of us really love Mansions, and try to ignore it's flaws and are really looking forward to an improvement! Here's hoping the app's fast, lean, and bulletproof!