The snippet below shows how the $args are gathered for an advanced search. The Instrument and Doctype items are checkboxes -- meaning that if multiple items of each are checked, the request object returns a comma-delimited list of IDs. The issue is that whatever I put into $args['category__and'] (and I've tried here just using $args['cat'], too)…

advanced_query_snippet.php

<?php 
// Check if results should be filtered
$search_filter = $_REQUEST["search_filter"];
$search_keyword = $_REQUEST["search_keyword"];
$search_instrument = $_REQUEST["search_instrument"];
$search_doctype = $_REQUEST["search_doctype"];

echo "<br />search_filter: " . $search_filter;
echo "<br />search_keyword: " . $search_keyword;
echo "<br />search_instrument: " . $search_instrument;
echo "<br />search_doctype: " . $search_doctype ;				
echo "<br /><br />";

// ............ more stuff here

// if the search filter is used 
$paged = (get_query_var('paged')) ? get_query_var('paged') : 1;
$args = array(
  'post_status'      => 'publish',
	'posts_per_page'      => 20,
	'paged'      => $paged,
	'order' => 'ASC',					
	'meta_key' => 'support-file-url',
	'orderby'   => 'meta_value, post_title'				
);	

// add on custom query info               
if($search_instrument != "" && $search_doctype != "")
{				
	// for testing
	print_r ($search_instrument);
	print_r ($search_doctype);
	
	$merged_arrays = array_merge($search_instrument, $search_doctype);	
	print_r ($merged_arrays);	
	
	
	$args['category__and'] = array_merge($search_instrument, $search_doctype);																																			
}
else if($search_instrument != "" && $search_doctype == "")
{
		$args['category__and'] = $search_instrument;							
}	
else if($search_instrument == "" && $search_doctype != "")
{
		$args['category__and'] =  $search_doctype;																
}
else if($search_instrument == "" && $search_doctype == "")
{
	$docttype_cats = get_categories("child_of=137");  // if no category selected, get all posts associated with the document categories	
	$cat_list = "";				
	foreach ($docttype_cats as $category) {						
		$cat_list .= $category->cat_ID . ",";
	}		
	$cat_list = substr($cat_list,0,strlen($cat_list)-1);	
						
	$args['cat'] = $cat_list;																		
}	

// add on keyword 
if($search_keyword != "")
{
	$args['s'] = $search_keyword;
}						

// output filter details if testing enabled				
if($_REQUEST["test"] == "yes")
{
	foreach ($args as $key => $value)
	{
		echo "<br />" . $key . ": " . $value;
		
		foreach ($value as $key2 => $value2)
		{
			echo "<br />--" . $key2 . ": " . $value2;
		}		
	}			
  echo "<br /><br />" . $GLOBALS['wp_query']->request; 
}	

query_posts( $args );		

// ............ more stuff here, display, etc.

?>