Basic form validation script Is this a good form validation script?

$(document).ready(function() {

    $("form").submit(function() {

        var shouldSubmit = true;

        $(this).children(":input:not(:button, [type=\"submit\"], [type=\"reset\"])").each(function() {

            if ($(this).val() == "")
            {
                shouldSubmit = false;
                return shouldSubmit;
            }

        });

        if ($("input:checkbox").length &gt; 0)
        {
            if ($("input:checkbox:checked").length == 0)
                shouldSubmit = false;
        }

        if ($("input:radio").length &gt; 0)
        {
            if ($("input:radio:checked").length == 0)
                shouldSubmit = false;
        }

        if (shouldSubmit == false)
            alert("All form fields must be filled out.");

        return shouldSubmit;

    });

});
The if statements could be cleaner:

    if ($("input:checkbox").length &gt; 0 &amp;&amp; $("input:checkbox:checked").length == 0)
    {
        shouldSubmit = false;
    }

    if ($("input:radio").length &gt; 0 &amp;&amp; $("input:radio:checked").length == 0)
    {
        shouldSubmit = false;
    }

    if (!shouldSubmit)
    {
        alert("All form fields must be filled out.");
    }