I'm sure this has been discussed and is being worked on (I did see some mentions of notification system plans in the DevBlogs and portal), but I just wanted to chime in and say that I'm eagerly awaiting the day that the app is able to push a notification letting me know that my current travel or action is complete!
I recognize that this feature is likely more tricky than it seems, as the app would need to occasionally check steps vs current action even when it's not open, increasing resource usage and battery drain, though I could be way off base here, as I'm not too familiar with the intricacies of mobile app development.
I wonder whether, upon the app being closed or minimized, it could pass the number of steps remaining in whatever task to the device's step logging api or a minimal step timer widget of some sort, then roughly handle it without having to constantly query the game server itself.
It's not terribly vital, considering the presence of the "saved steps" system, but I'm still looking forward to it. It'll be a nice reminder to keep moving and progressing!