Plugin that checks if user has permissions to publish pages/posts/custom post types. If they don't, it will send it to review by someone who can
Approval Workflow is meant to create a workflow process in WordPress. This plugin adds a box to the post edit screen when a user does not have publish permissions for that post type. It also allows you to set a WordPress role as the approvers. Note: this role must have publish permissions. The approvers get notified by email when someone has submitted something to the workflow. This works on WordPress Multisite too.
If you need help setting up the roles, I'd recommend the Members plugin.