Theme_My_Login_Form::render_errors()

public function render_errors() {

    if ( ! $this->has_errors() ) {
        return;
    }

    $errors   = array();
    $messages = array();

    foreach ( $this->errors->get_error_codes() as $code ) {

        $severity = $this->errors->get_error_data( $code );

        foreach ( $this->errors->get_error_messages( $code ) as $error ) {
            if ( 'message' === $severity ) {
                $messages[] = $error;
            } else {
                $errors[] = $error;
            }
        }
    }

    $output = '';

    if ( ! empty( $errors ) ) {
        $output .= sprintf(
            '<ul class="tml-errors"><li class="tml-error">%s</li></ul>',
            apply_filters( 'login_errors', implode( "</li>\n<li class=\"tml-error\">", $errors ) )
        );
    }

    if ( ! empty( $messages ) ) {
        $output .= sprintf(
            '<ul class="tml-messages"><li class="tml-message">%s</li></ul>',
            apply_filters( 'login_messages', implode( "</li>\n<li class=\"tml-message\">", $messages ) )
        );
    }

    return $output;
}

View src/includes/class-theme-my-login-form.php, line 396 on GitHub