[Matt@Sim_Moves]

There are some really good instructions on how to get the "Cagney" update, posted from Criterion forum-user Xpowaspa:

Step One: Don't start the game
Before you can get the update you need to either exit the game or not insert it. As it won't auto-update (or will it?)

Step Two: Go to the marketplace
Right now it should be in New arrivals > Burnout Paradise but for a later date I think you can find it in Game Add-ons > All(?) > Burnout Paradise.
NOTE: XBL Silver users will have to wait at least another week at this moment. If you want to blame someone... blame Microsoft

Step Three: Download the update
And do something to waste the time....

Step Four: Start the game
You should get a prompt to update the game. If you have problems try clearing your cache and see if that helps (NOTE: You will need to update all your games again if you do this)

Step Five: You're done
Now go play Cagney. You have to wait for the Rai-Jin and Olympus though...