Looks OK. It's not on your diagram so I don't know if you were going to do it, but you can trunk between your switches and your firewalls too. This way you can have many DMZs over one physical link (bandwidth permitting).
You can safely put some IP addresses on the public switches in the provate range and create a DMZ for administration and only allow ssh access to the switches for example. Turn of things like cdp and put access-lists also on the switches i.e. you don't need punlic IP addresses on the switches. With access-lists and username/passwords (with radius or tacacs if you have it - but you will have to remeber to allow that through the firewall as well), provate IPs, and in a DMZ for admin, you should be ready to go.
Regards,
Ian
