The DNS server will see the changes when the IP addresses re-register.
The way I do a change is to actually shutdown things - particularly with Exchange. So stop all the Exchange services, then change the IP address, DNS etc and shutdown the server. Then change the domain controller and reboot it.
Once the DC is up, bring the Exchange server up.
Everything else can be restarted to pick up the new settings.
MX record - the internet isn't to know. Just ensure the router is reconfigured with the new internal IP address for the port forwarding.
Mentioning DHCP, if you were clever and did the planning in advance with reservations (can all be done in advance, simply do not activate the scope) you could set the entire site to DHCP, except for the domain controllers. You would need to collect MAC addresses etc.
Then simply activate the scope and set everything to DHCP. They will get their settings automatically. Can save lots of time if you have a small panel to enter the settings on a print for example.
I now have two clients on an exclusive DHCP setup and it works very well. I want to change a DNS server takes me ten seconds rather than an hour or two to change all the printers etc.
Simon.