Is it possible to give a custom post type its own category box?
If I use 'taxonomies' => array("category") or register_taxonomy_for_object_type('category', post_type); I get the desired box but it shows all categories across all post types.

I want the displayed values in the meta box to show just that post types categories.
If I use:
register_taxonomy( 'categories',
array (
0 => 'event',
),
array(
'hierarchical' => false,
'label' => 'Event Categories',
'show_ui' => true,
'query_var' => true,
'rewrite' => array('slug' => ''),
'singular_label' => 'Event Category'
)
);
then I have to manually type tags opposed to being able to click a checkbox to assign categories.

This breaks the UX for less computer savvy people.
Is there a better way?
register_taxonomyfor archival purposes. Added pictures to help further illustrate the actual question. – tr3online Dec 10 '12 at 21:01