Here's my wishlist in order of priority.
Basic functions to be on par with the browser experience: flag comments as being from a mod, make sticky posts in a community, view reports, remove comments and posts, lock posts, ban users. Make sure there's a field to enter the reason for the removal/ban, to be recorded in the mod log.
Additional features above and beyond the basics (I have suggested these to other app developers):
Summit does.
I'm told Sync does, though I haven't tried that app yet myself to confirm.
Mod tools are on the roadmap for Voyager and several other apps.
Confirming that Sync does have basic mod tools (lock, pin, remove posts, ban user from community) Assuming there will be more added in the future.