You have to insert the CoD disk and log into Live to get the update.
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Official Press release:
Infinity Ward and Activision have issued a Title Update that addresses the player progression loss issues associated with Call of Duty 2 on the Xbox 360. The team is continuing to work on additional updates and we will keep you posted."
Keep in mind that this patch pertains to the single-player campaign ONLY Infinity Ward is still working on a patch to address the lag issues currently found in the multiplayer modes.
Well have more information on the multiplayer patch as it becomes available.
From here:
http://news.teamxbox.com/xbox/10157/Call-of-Duty-2-Patch-Now-Available/