With the recent upgrades to the forum I have been getting a lot of 404 not found pages because the url has changed. I am not complaining but I think it would be great if we could add a Forum Search Bar to our wordpress 404 page so we could say something like:

Didn't find what you were looking for? Please search the forum.

leaving aside the issue of whether it was right or wrong to make this change you can actually add anything you like to your WP 404 page. Customisation like this is one of WP's major strengths.

in other posts I have also mentioned that you can make your site a 'Smart Site' by installing Redirection plugin by John Godley.

You will have to manually install the redirection regex, but the plugin makes it much much easier.

Actually what I was hoping for is the necessary code to add there as I wouldn't know where to start.