How do I give the permission to add points, but not to moderate them?
In Drupal 6, there is no easy way to do that. It might work if you implement hook_menu_alter() in a custom module and add a different permission in access arguments that the default.

It might not help you at this point, but I have taken over that module for Drupal 7 and we have improved it a lot. Among many other things, it now has separate add/edit and moderate permissions which allow for fine-grained access control. So if you are just starting your site, you might want to consider using Drupal 7 instead.