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):

• Remember to clearly indicate which posts have been removed. Lemmy's default behavior leaves removed posts visible to mods,
• Have an option to hide removed posts' thumbnails and/or titles from the mod's view. Nobody wants to keep seeing some grotesque troll post that was removed from public view days prior.
• Add a Moderated Communities feed. For people who mod multiple communities this makes it easier to quickly check in on recent activity.
• Implement push notifications for reports.

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.