If a host is known by multiple addresses, then every service on this host can be referred to by multiple names! Addressing this host requires picking one of these. Since the packet is addressed to the interface and not the host, path information is introduced into the address. The exact ramifications of this effect depend heavily on the network design. In particular, careless design can result in a host becoming reachable by one address but not by another. The simplest solution to this problem is to select the host's most reliable interface and advertise its IP address as the host's primary IP address.
In addition to the Encyclopedia's resources, Chuck Semeria has written an excellent paper on Understanding IP Addressing.