You can test the development (and unstable!) packages of MATE Desktop 1.5, they are already available for some distributions. Obviously, dont use them in a production machine 
List of new features and changes in 1.6 is available on MATE wiki
Debian Wheezy
You can add deb http://dev.mate-desktop.org/debian wheezy main to your /etc/apt/sources.list.
Ubuntu Quantal
You can add deb http://dev.mate-desktop.org/ubuntu quantal main to your /etc/apt/sources.list.
Fedora 17+
1.5 packages, also if unstable, are already on official Fedora repositories.
openSUSE
1.5 packages are available through OBS: https://build.opensuse.org/project/repositories?project=X11:MATE
Archlinux
You can build 1.5 packages using PKGBUILDs from https://github.com/mate-desktop/archlinux-packages.
Ubuntu repository says this error:
” NO_PUBKEY 68980A0EA10B4DE8″
I can’t install it.
You need to install the package mate-archive-keyring from the stable MATE repository.
Now I fixed it with:
sudo apt-key adv –keyserver keyserver.ubuntu.com –recv-keys 68980A0EA10B4DE8
Anyway…
MATE developers are doing a great job! MATE is my favourite DE
P.S.: Nice GNU nycan-cat style in “about MATE”, I tested it in fedora 18.
Why the package python-mate-desktop removed?
This package is extremely reliable for attaching the panel applet that uses python.
python-mate-desktop is removed due to migration to GSettings. Python applets need to be migrated to use Introspection (http://wiki.mate-desktop.org/docs:devel:mate-panel#python_applets). I’ll write a post about this soon.