The problem with the database schema as implemented is each node has parent_id in it. If you want the node to appear in two forums, you'd need two parent_id fields. If you want the node to appear in three forums, you'd need three, and so on. That won't work.
What will work is if you break node into two tables. One has parent_id and node_id, and the other has node_id and rest of node. Let's call the first table Node and the second NodeData.
This query selects a complete node for forum # in #forum_id:
SELECT * FROM Node,NodeData WHERE Node.parent_id=$forum_id AND NodeData.node_id=Node.node_id
This query tells you where the node $node_id is cross posted:
SELECT * FROM Node,NodeData WHERE Node.node_id="$node_id" and NodeData.type="FORUM" and NodeData.node_id=Node.parent_id
While I'm at it, most things could be NodeData. Forums, Posts, Threads, and so on. You have NodeData.type tell you which type the node is.
This leads to the idea that a Node can be a Thread or any kind of new data type. A Resource, a Media object, a Review, and so on. But even better, they could be a Blog post or a Wiki Page.
I'd love to see the last two implemented. You already have a "program" that views Threads. So the system would be extensible to have programs that view the various other types.
A Blog post would appear in the list of threads. You create them like you do a thread, but the form may be custom for what a new blog post would contain. The Blog view program would show the blog first post and the comments in reverse chronological order (newest first). A Thread view program shows then oldest first.
A Wiki page would appear in the list of threads, too. You create them and anyone with permissions can edit the page (first post).
You'd identify the various node types in the forum listing by an icon to the left of the title.
3rd party plugins can provide an infinite number of new node types and programs to view and edit them, since the type field is a string.
Any forum could have a "blog view" and a "forum view."
We're all familiar with the forum view. The blog view would render a page with 20 threads. Each thread would be shown as full first post (or some first part of it) with "# of comments" displayed below it. It would look like WordPress, and rather trivial to implement.
I've mentioned elsewhere that I run a sports site and my users tend to congregate in threads during games. The way it works now, Portland Trail Blazers fans can be in their game thread and Boston Celtics fans can be in their game thread. If the Node/NodeData scheme is implemented, they can be in the same thread together, the Blazers posters seeing the Blazers forum skin (determined by Node.parent_id) and the Celtics forum poster see the Celtics forum skin.
Use these ideas, or don't use them. I offer them for free