A few suggestions/observations

1.  Under Reports tab, when you "find something of interest" there is a button that says "see on map."  It would be helpful if it took you to the location of the discovery.

2.  After placing the hero flag, if you leave that screen (e.g. go to world) the hero stops moving.  My preference would be for the hero to go where the flag is regardless of the active screen.

3.  When you are on the world screen domain view, it would be helpful to put an icon on the town that the hero is currently residing in.

4.  It may be just me, but the little discovery icon for iron looks like my hero didn't clean up after her dog :)

I agree with all those. 

You are only required to click on a town to find a hero unless hero is fishing or meditating.

My preference is that if I am directing my hero in town to a specific place, I prefer her not to arrive when I am not there. Delaying the hero/army until I return to that town allows me to control where the hero is at all times. If in the future she is able to die in battle against monsters, I do not want this to occur while I am fooling around somewhere else, only to come back to a dead hero.