Mac App Store: we could not complete your update the server gave an error during download: 403 Forbidden

Edited to add

Based on the comments on this answer, it appears that Xcode updates via the system Software Update were delayed, appearing quite a bit after they became available for manual download from the developer portal.

It may even be that Apple fits them into times when their network usage was low, which could delay an update even if you clear out your old copy and reinstall the not-quite-up-to-date version. Perhaps the update would appear if you waited several days.

Previous answer

Xcode has never, ever updated for me through Software Update, and it's never updated for the dozen or so developers I work with. The Apple employees that I follow on Twitter -- guys like Jake Behrens, Michael Jurewitz (the dev tools evangelist), Chris Hanson, and Bill Bumgarner -- along with former Apple employees who are devs and other high-profile devs I follow, all tweet something along the lines of, "hey devs, time to visit the developer portal to download the new version of Xcode" when an update comes out.

Are you absolutely certain Xcode updates are arriving automatically for your coworkers? Have you seen it happen? Are you sure they're not pulling your leg? I've certainly never heard of it and consistently hear the opposite, so it sure seems unlikely to me.

The only automatic Xcode updating I'm aware of for Xcode 4, and only then if it was purchased through the Mac App Store and not downloaded from the portal, and only then if you launch the App Store and click on the update, which really isn't very automatic.

I seem to have fixed the problem.

I used opensnoop to follow all file accesses while the app store was running. I spotted that ~/Library/Cookies/com.apple.appstore.plist was being accessed - this file had not been deleted by Safari when I cleared all cookies! The file had incorrect permissions - I deleted it. Now the App Store seems to be working again.

Opensnoop is a great tool!