Disabling 3rd party cookies has never broken a single site for me. I've heard that some banks require them, though.
As for Self-Destructing Cookies: it's a pretty drastic measure. Considering this, it's surprisingly compatible. Among the sites that I frequent, not a single one stopped working. Inter-domain transaction - e.g. a shop forwarding you to Paypal and back - used to be a problem, but the latest version has a heuristic for that. Still, I'm pretty sure that some people will experience fallout. You can work around that; SDC has numerous functions that can help in such cases (pause, undelete, whitelist for session).