The 17th Month of Apple Bugs issue is a buffer overflow in the legacy SLP daemon. The code in question manages local service registrations on the /var/run/slp_ipc unix domain socket, and the vulnerable appears to be local only.
The buffer overflow is in SLPInternalProcessHandlerThread::HandleCommunication()'s kSLPRegisterURL/kSLPDeregisterURL handler:
char attributeList[1024] = ""; ... memcpy( &attributeList[strlen(attributeList)], attributeListPtr, attributeListLen );
If you're concerned about the issue, disabling SLP is straight-forward, and should not result in a loss of functionality for most users. SLP has not been used for service registration since Mac OS X 10.2, and the slpd daemon is used only to register and announce SLP services to legacy clients. As far as I'm aware, SLP is only started when "Personal File Sharing" is enabled -- however, you won't need to disable File Sharing to disable SLP.
To disable slpd, open /Applications/Utilities/Directory Services.app and deselect "SLP" in the "Services tab. You can re-enable slpd in the same way. To make sure that the SLP daemon is stopped, restart your computer or kill the daemon from Terminal.
Thanks to 'MaxP' of the MoAB Fixes group for determining when, and how, slpd is started.