The easiest solution would be to enable the moderation features on the folder. Then when somebody posts somethings, a reviewer would have to approve the post before it is visible to others in the folder.
Otherwise, you'd have to write a macro to copy to every user's PC (or write a COM Add-In). This code could track every PostItem that is opened by setting a PostItem object reference declared With Events whenever the Inspectors.New_Inspector event is fired.
Then you can trap the PostItem_Send or Reply events (I'm not sure which, this is tricky), and evaluate whether the MAPIFolder object in the Parent property is the Public Folder that you need to manually moderate. If it is, only allow replying or sending if the ConversationIndex or ConversationTopic properties are NOT empty. If they are, this indicates a new post. This may or may not be the proper approach - like I said, it's tricky - but with some playing around you *can* trap for only replied messages.
The only other thing to be aware of is that the presence of this code/add-in on a user's machine is basically a "big hammer" security mechanism which is better handled by the automatic folder moderation features.