Is there a delegate, callback, or other method that can be used to detect that the extent of the map has been changed in the ESRI iOS SDK?
According to the class reference for AGSMapView, there are two NSNotifications that are broadcast whenever the map pans or zooms to a new extent. Set up a listener for those notifications.
As answered already, you can use the 2 notifications: AGSMapViewDidEndPanningNotification and AGSMapViewDidEndZoomingNotification
however, if you need more immediate feedback you can add an observer to the AGSMapVeiw's visibleAreaEnvelope property:
Then you can react to that change like so: