Exchange Server 2003 & DNS Problems

I’m having some problems setting up an Exchange server, and I think it’s because I have my DNS server set up incorrectly. I have an A record set up for mydomain.com, and then a CNAME record set up for mail.mydomain.com. When I do an nslookup on mail.mydomain.com, I get the correct (local) IP of 192.168.0.1, however when I try to ping mail.mydomain.com, it doesn’t work because it’s trying to ping the global IP of the server. This doesn’t make a lot of sense to me. Any ideas?

From a client computer, all of the emails I try to send to another local user get bounced back with this error:

#5.1.8 smtp;553 5.1.8 … Domain of sender address sender@servername.local does not exist>

Thanks in advance,
Scott