I'll repost my reply from "Compensation for Cancelled flights" under the Coupon Connection regarding a cancelled MIA-LAX on a MIA-LAX-SYD reservation:

If the flight was cancelled due to mechanical problems, they should have re-routed you onto another airline. Were no flights available on any airline, or no flights on the airline you reserved? They aren't obligated to give you a voucher, but they should cover your hotel and meal expenses.
If you are writing after the fact, though, I don't think they'll go back and do anything, since you were supposedly satisfied with the resolution at the time.

This may vary depending on if you had a single ticket for the whole Miami-LA-Sydney, or if you had LA-Sydney on, say, Qantas, and later bought a one way Miami-LA on American. If you had 2 separate tickets, the airline that cancelled the flight is responsible for getting you to your ticketed destination (LA), but isn't responsible for connections on separate tickets.