If you want regular users to be able to moderate threads and posts in the simple forum module, you will just need to set that permission in the user's details area:
Go to Contacts > Manage Contacts > View Contacts > Edit the user you want.
Then on the member's details page, click on the Profile > Permissions tab to enable the Allow Forum Moderation permission.
Once you have done that, whenever the user logs in, he can view threads that still need approval, while others cannot.
