Yep, I wasn't able to install the Command Line Tools from the Xcode Preferences. It works if you do it manually ... by downloading the Command Line Tools from:
Same here; the late July update is only installable on 10.7. Looks like we're still stuck waiting for Apple to sort out the 403 error for XCode 4.4 on Mountain Lion.
For whatever it may be worth, installing from the preferences worked fine for me. I heard other reports of failures, though, and assume it's related to the massive number of people all trying to download Mountain Lion at once.
That page only shows me the downloads for Xcode 4.3 and 4.5 Developer Preview, but it looks like I can use the 4.4 versions just fine by adding "/Applications/Xcode.app/Contents/Developer/usr/bin" to my $PATH
I couldn't get /Applications/Xcode.app/.../usr/bin/gcc to work for me today. It could not access stdlib includes and such. I got the Xcode preferences installer of the command-line tools to work, and that put a gcc in /usr/bin/ that worked completely. I don't know what's different between the two, but that seems to be the official way to do it.
Kudos to Apple for the self-contained command-line tools package download. Hopefully that'll continue with another update for 10.8.