How to intercept a 404 error

I’d like to intercept 404 errors and do some things before to show the 404 error page.

How can intercept the 404 error?

As was mentioned in a comment, template_redirect would be an appropriate hook for intercepting a 404 before the template is loaded.

function wpd_do_stuff_on_404(){
    if( is_404() ){
        // do stuff
    }
}
add_action( 'template_redirect', 'wpd_do_stuff_on_404' );

Refer to the Action Reference for the general order of actions on the front end. The main query runs between the posts_selection and wp actions, so that is the earliest you can determine that a request is a 404. The template is then loaded after template_redirect, so it’s too late to set headers after that point.