Very helpful information, but it brings another question to mind. Would it be possible for the 'cheater' (for lack of a better term) to choose which transaction got confirmed after the result of satoshidice was shown? I'm sure its either impossible or already figured in somehow, but it would create major issues if not.
When your node sends out a transaction it broadcasts it to nodes it is connected to, and they broadcast it to nodes they are connected to, etc. The nodes take the first valid transaction in which a coin was used and ignore any others. Miners will, within seconds, have the first transaction and that will eventually make it into a block.
So yes, if you happen to be mining you can broadcast to the network one transaction and then include in your own mining block a double spend to yourself for each of other transactions in that same block that you wish to see vaporized.