I agree that the United app is awesome. It provides so much information (seat map, upgrades, inbound aircraft tracing) and is pretty easy to use. I'm also pretty impressed by the ability to search for and book flights natively within the app. A big thumbs up for me.
I recently provided feedback that I'd like to see expert mode fare buckets on the app. Also, as others have mentioned, it'd be nice to be able to change/cancel flights within the app. Maybe also redeem upgrades or pay for upgrades before 24h before the flight.