Does raising the functional level of a Windows Server 2003 Active Directory (AD) forest cause any side effects that relate to Exchange Server?
The answer to your question depends on the original forest functional level and on the version of Exchange that you're using. I'm presuming that you started with a Windows 2000 forest, then upgraded all the domain controllers (DCs) in the forest to Windows 2003—a prerequisite to raising the forest functional level to Windows 2003. That leaves the question of which Exchange version you're using.
If you're using Exchange Server 2003 exclusively, raising the forest functional level is a safe move and won't affect Exchange. However, if you're using Exchange 2000 Server in your organization, the Exchange 2000 Active Directory Connector (ADC) and Recipient Update Service (RUS) won't work properly after you raise the forest functional level because doing so changes the way that replication works for objects to which multiple linked values are attached. Group objects are a prime example. Linked value replication (LVR) reduces the replication overhead necessary to replicate group-membership changes but also confuses the Exchange 2000 ADC and RUS, so that membership changes don't replicate properly. Therefore, if you have any Exchange 2000 servers in your organization, be sure to update all your ADCs to the Exchange 2003 version and upgrade to Exchange 2003 any Exchange 2000 machines that run RUS before you raise the forest functional level.