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
You can add deb
http://dev.mate-desktop.org/debian wheezy main to your
You can add
deb http://dev.mate-desktop.org/ubuntu quantal main to your
1.5 packages, also if unstable, are already on official Fedora repositories.
1.5 packages are available through OBS: https://build.opensuse.org/project/repositories?project=X11:MATE.
You can build 1.5 packages using PKGBUILDs from https://github.com/mate-desktop/archlinux-packages.