We are looking at having one of our DAG partners in a separate location at another company and would like to encrypt the whole server.

Should be local disk.

Anyone used bitlocker in this instance and know of any common issues or gotchas?

Its supported. There will always be a small performance overhead associated with it, but otherwise, go for it. I would ensure you follow all the Bitlocker Best Practices of course

http://technet.microsoft.com/en-us/library/ee832792(v=exchg.150).aspx

http://blogs.technet.com/b/wincat/archive/2010/09/09/bitlocker-protected-exchange-server-2010-deployment-an-interesting-case-study.aspx

http://technet.microsoft.com/en-us/library/jj592683.aspx