There are no DNS changes required. All that's needed to change the mailflow is redirect port 25 so it is no longer going to the 2003 server but is going to the 2010 server instead.
Either way the Exchange organisation will deal with the appropriate delivery. A few things to checkout when you do swap it over. By default the Exchange 2010 receive connector doesn't allow anonnymous connections you will need to set this otherwise mail will be rejected.
Another common issue is a smarthost configured on the default SMTP Virtual server on the 2003 server. Check out my article here:
http://www.experts-exchange.com/articles/Software/Server_Software/Email_Servers/Exchange/Exchange-Server-Mail-Flow.htmlI also have a migration guide here:
http://www.experts-exchange.com/articles/Software/Server_Software/Email_Servers/Exchange/Migrate-Small-Business-Server-2003-to-Exchange-2010-and-Windows-2008-R2.html it's written for SVS2003 but the exchange and Active Directory parts are exactly the same.
And finally if you plan to use DAG make sure you are using Enterprise edition of Windows Server (you don't need Exchange Enterprise). I have also written a DAG guide here:
http://www.experts-exchange.com/articles/Software/Server_Software/Email_Servers/Exchange/High-Availability-Exchange-2010.htmlthere are a few links but they are my articles and I think quite specific :)