Custom Taxonomies not appearing in Admin

There seemed to be an issue with the way you registered the taxonomy.
I prefer to register the taxonomy first, before registering the post type.

I submitted a pull request but here ya go:

<?php

// hook into the init action and call create_book_taxonomies when it fires
add_action( 'init', 'create_ksasexhibits_taxonomies', 0 );

// create two taxonomies, genres and writers for the post type "book"
function create_ksasexhibits_taxonomies() {
    // Add new taxonomy, make it hierarchical (like categories)
    $labels = array(
            'name'                  => _x( 'Exhibition Types', 'taxonomy general name' ),
            'singular_name'         => _x( 'Exhibition Type', 'taxonomy singular name' ),
            'add_new'               => _x( 'Add New Exhibition Type', 'Exhibition Type'),
            'add_new_item'          => __( 'Add New Exhibition Type' ),
            'edit_item'             => __( 'Edit Exhibition Type' ),
            'new_item'              => __( 'New Exhibition Type' ),
            'view_item'             => __( 'View Exhibition Type' ),
            'search_items'          => __( 'Search Exhibition Types' ),
            'not_found'             => __( 'No Exhibition Type found' ),
            'not_found_in_trash'    => __( 'No Exhibition Type found in Trash' ),
        );

        $args = array(
            'labels'            => $labels,
            'singular_label'    => __('Exhibiton Type'),
            'public'            => true,
            'show_ui'           => true,
            'hierarchical'      => true,
            'show_tagcloud'     => false,
            'show_in_nav_menus' => false,
            'rewrite'           => array('slug' => 'exhibiton', 'with_front' => false ),
         );
    register_taxonomy( 'exhibition_type', 'ksasexhibits', $args );
}

function register_ksasexhibits_posttype() {
    $labels = array(
            'name'              => _x( 'Exhibits & Programs', 'post type general name' ),
            'singular_name'     => _x( 'Exhibit', 'post type singular name' ),
            'add_new'           => __( 'Add New Exhibit & Program' ),
            'add_new_item'      => __( 'Add New Exhibit & Program' ),
            'edit_item'         => __( 'Edit Exhibit & Program' ),
            'new_item'          => __( 'New Exhibit & Program' ),
            'view_item'         => __( 'View Exhibit & Program' ),
            'search_items'      => __( 'Search Exhibit & Program' ),
            'not_found'         => __( 'No Exhibit & Program found' ),
            'not_found_in_trash'=> __( 'No Exhibit & Program found in Trash' ),
            'parent_item_colon' => __( '' ),
            'menu_name'         => __( 'Exhibits & Programs' )
        );

        //$taxonomies = array( 'exhibition_type' );

        $supports = array('title','revisions','thumbnail' );

        $post_type_args = array(
            'labels'            => $labels,
            'singular_label'    => __('Exhibit & Program'),
            'public'            => true,
            'show_ui'           => true,
            'publicly_queryable'=> true,
            'query_var'         => true,
            'capability_type'   => 'post',
            'has_archive'       => false,
            'hierarchical'      => true,
            'rewrite'           => array('slug' => 'exhibitons', 'with_front' => false ),
            'supports'          => $supports,
            'menu_position'     => 5,
            //'taxonomies'      => $taxonomies,
            'show_in_nav_menus' => true
         );
    register_post_type('ksasexhibits',$post_type_args);
}
add_action('init', 'register_ksasexhibits_posttype');

function define_exhibiton_type_terms() {
    $terms = array(
        '0' => array( 'name' => 'Campus Partnerships','slug' => 'campus'),
        '1' => array( 'name' => 'Community Partnerships','slug' => 'community'),
        '2' => array( 'name' => 'Independent Study','slug' => 'independent'),
        '3' => array( 'name' => 'Digital Work.','slug' => 'digital'),
        '4' => array( 'name' => 'Mellon Foundation','slug' => 'mellon'),
        );
    return $terms;
}

function check_exhibition_type_terms(){

    //see if we already have populated any terms
    $terms = get_terms ('exhibition_type', array( 'hide_empty' => false ) );

    //if no terms then lets add our terms
    if( empty( $terms ) ){
    $terms = array(
        '0' => array( 'name' => 'Campus Partnerships','slug' => 'campus'),
        '1' => array( 'name' => 'Community Partnerships','slug' => 'community'),
        '2' => array( 'name' => 'Independent Study','slug' => 'independent'),
        '3' => array( 'name' => 'Digital Work.','slug' => 'digital'),
        '4' => array( 'name' => 'Mellon Foundation','slug' => 'mellon'),
        );
        foreach( $terms as $term ){
            if( !term_exists( $term['name'], 'exhibition_type' ) ){
                wp_insert_term( $term['name'], 'exhibition_type', array( 'slug' => $term['slug'] ) );
            }
        }
    }

}

add_action ( 'init', 'check_exhibition_type_terms' );

?>