As per my understanding there are two issues,
- A subset of users can't see updates on files
- They are unable to publish files
I would check the following things,
- User will not be able to see update if the update is done by other user and is not published. So the specific documents are checked out to other users or not.
- If item level permission is being set in the specific documents, if permission inheritance is broke for specific item and the user in question don't have permission in the item level.