It looks like the Deer Park Check For Updates option now works. However you have to change the url that it uses to check for the latest version. You can use the about:config url to change the setting: app.update.url. The url to use is:
/0/%PRODUCT%/%VERSION%/%BUILD_ID%/%BUILD_TARGET%/%LOCALE%/update.xml
Once changed, just close Deer Park and start it up again. Go to Tools – Options – Advanced – Update – and click on the Deer Park Check now option. If Deer Park is not uptodate, it will ask you to download the latest version and then ask you if it is okay to restart Deer Park.
The update check for extensions is also changed in Deer Park, and instead of showing you one progress bar for all the extensions, it brings up the extension list and shows you each one that is being updated. It is pretty slick compared to Firefox’s current implementation.
I should note that I am testing Deer Park on Windows only. The Mac OS X version is not quite as stable, and even the Windows build tends to crash without warning, but it is getting better by the update.