What’s wrong with my usage of add_filter

I cleaned up your code, and put all the header information for installing it. Your plugin works fine, I tested it!

/*
Author: whoever
Plugin Name: Some Name
Plugin URI: 
Text Domain: some-domain
Version: 1.0
*/

function DynamiteSearch($form) 
{
    $form = "<form method = 'get' id = 'searchform' action = ' ".site_url()." ' >";
    $form .= "<div><label class="hidden" for="s">". __("Search for: ") . "</label>";
    $form .= "<input type="text" value=" ". attribute_escape(apply_filters("the_search_query', get_search_query())) ." ' name="s" id='s' />";
    $form .= "<input type="submit" id='searchsubmit' value=" ".attribute_escape(__("Look for it'))." ' />";
    $form .= "</div>";
    $form .= "</form>";

    return $form;
}

add_filter('get_search_form', 'DynamiteSearch');

Try changing the submit button text to see if it works. Let me know if it worked for you.

Thanks,
Rutwick