Chrome doesn't accept the certificate when the trailing dot is in the request.
I bet if you configured your site to redirect to a URL with a trailing dot, it would break a lot of badly written robots. I'd be interested to hear about how it affects the major search engines before I'd want to implement it on any important sites.
EDIT: I learned something new today, adding the trailing dot can be a good idea:
http://homepage.ntlworld.com./jonathan.deboynepollard/FGA/we...