How does: /index.php?post_type=event&event-date=2011-07-25 work? What if it doesn’t work?

You will have to use the rewrite API to get that to work. First you need to register the rewrite rule.

add_action( 'init', 'wpse23712_rewrites' );
function wpse23712_rewrites()
{
    add_rewrite_rule( 'events/day/(\d{4}-\d{2}-\d{2})/', 'index.php?post_type=event&event_date=$matches[1]', 'top' );
}

Then add your event_date to the query vars so wordpress understands it.

add_filter( 'query_vars', 'wpse23712_vars' );
function wpse23712_vars ( $vars )
{
    $vars[] = 'event_date';
    return $vars;
}

Then on the front end (in your archive-event.php) you can grab the event date with get_query_var() and use it in your query. I’d suggest you store something with a custom field (in the wp_postmeta table) for each even with the ISO formatted date. Then you can run a meta_query to retrieve those event posts.

So when someone navigates to yoursite.com/event/day/2011-07-28/ it will show events for that day.

I didn’t test the above, but you should able to take it from here.