One thing I always wondered is how session persistence is maintained for things like webapps when trying to host services through anycast. Only idea I can dream up is cookie based and involves each site having internal proxy mappings to each pop in the event a different pop becomes the favored route (paths change all the time, and routers on the internet dont care that you had an established connection).
What you're asking about isn't really an anycast problem either, you can have the same situation with any load balancing situation; if you need the client to come back to the same server, you need the client to bring you back something that says which server to route to, for example a cookie or a hostname, and you need something in your stack that handles that and routes it (could be DNS entries, a hardware or software load balancer, application logic, etc). Avoiding sessions is better, of course, if you can (or if you can have the client keep the state information; possibly encrypted and signed).