How to prepend to the_title for admin-side plugin’s use

The problem is global $post.
As @Pieter suggested global $post object can be alter anytime with some other plugin or code. Menu items are effected because global $post does not contain the correct object.

Instead of $post, the_title filter also provide you ID of current post in action, so use it in this way

function append_album_review_to_title( $title, $id ) {
    if ( get_post_type( $id ) == 'album_review' ){
        return 'Album Review: ' . $title;
    } else {
        return $title;
    }
}
add_filter('the_title', 'append_album_review_to_title', 10, 2);