You may want to look at chaining the jQuery.stop() command before each animate command. It stops all the currently running animations on the specified elements.
i.e.
jQuery("#quickfind").stop().animate({
height:"200px", opacity: 1},"slow");
return false;
Is there a reason you are using jQuery instead of the shorthand $ for the jQuery object? you can use the $ shorthand for the jQuery object, even if using other libraries that use it, by following this pattern-
(function($) {
//Your code here using $ shorthand for jQuery :)
})(jQuery);
This means that $ within the scope of the outer function is a reference for the jQuery object.
I have set up your code on this sample page. If you want to edit it, then add "/edit" to the URL.
Also, Are you sure that "show" is a valid value for height and opacity?
My understanding is that height needs to be set to either auto(i.e. size of containing block), a length or a percentage relative to the containing block, and opacity should be a value between 0 and 1 (jQuery abstracts away differences between browsers and will use whichever opacity attribute is appropriate i.e. opacity or filter:alpha(opacity))