Custom Post Type and Breadcrumbs Conflict

Your custom post type matches the conditional is_single(), so this part is trying to output the category the post is assigned to, which I’m assuming doesn’t exist:

if (is_category() || is_single()) {
    $category = get_the_category();
    $crumbs .= '<span typeof="v:Breadcrumb"><a rel="v:url" property="v:title" href="'.get_category_link($category[0]->cat_ID).'">'.$category[0]->cat_name.'</a></span>';
}

either check if $category contains a category, or change is_single to just check the post post type:

if (is_category() || is_singular('post')) {