I'm currently playing around with different way of moderating posts. It has been suggested to me that I place users in the Contributor group (Role), should I want to use an approval process for posts. While the feature could be better, it's good enough for now. However, I need to be able to use my own customized Roles (using the "Role Manager" plugin), as I need more control over the restrictions. The supposed bug is that even if I create a Role that is identical to the contributor Role, users with that Role won't be able to have their drafts approved.
The fix would be to display every draft saved by every user who does not have the publish posts capability, instead of only those belonging to users with the Contributor Role.
A better fix would be to implement a better Post Moderation system (as has been suggested by others before), where a user without publishing rights has a "submit for approval" instead of a "publish" button, which would allow a user to save drafts without risking to have them published before completion. If a proper queue system is also implemented, it would help the admin/editor with the approval process too.