$.ajax({
                type: "POST",
                url: "mail.php",
                data: dataString,
                success: function(data) {
                    $(".contact-form").hide();
                    $(".alt-contact").hide();

                    // Depending on what the PHP script returned, display a message of success or error
                    if (data == 1) {
                        $(".contact-form").html("<div class='success-message'><div class='success-image'></div><div class='success-title'>Success! The message has been sent!</div><div class='success-body'>I'll get back to you right away.</div></div>");
                    }
                    else {
                        $(".contact-form").html("<div class='error-message'><div class='error-image'></div><div class='error-title'>Whoops! An error occurred.</div><div class='error-body'>I'll get back to you ASAP.</div></div>");
                    }

                    $(".contact-form").fadeIn(500);
                }
                error: function(jqXHR, textStatus, errorThrown) {
                    $(".contact-form").hide();
                    $(".alt-contact").hide();

                    // Inserts divs making up the success message for the form submission
                    $(".contact-form").html("<div class='error-message'><div class='error-image'></div><div class='error-title'>Success! The message has been sent!</div><div class='error-body'>I'll get back to you right away.</div></div>");

                    $(".contact-form").fadeIn(500);
                }
            });

$.ajax({
    type: "POST",
    url: "mail.php",
    data: dataString,
    success: function(data) {
        // code
    }, <----- Right there!
    error: function(jqXHR, textStatus, errorThrown) {
        // code
    }
});

$(".contact-form").fadeIn(500);
 } ,  <--------      Missing a comma here
 error: function(jqXHR, textStatus, errorThrown) {