I had the same type of problem with the 64-bit live image. Connecting to a wireless network requires a root password, as does accessing any HDD partition. The live installer silently fails, but I can force it to run through the terminal, but I still get access denied when the installer reaches the partitioning stage. It's a bloody mess, but no one else was reporting these issues on the forums here, so I concluded that I was experiencing a bizarre quirk on my end.
The XFCE version works flawlessly, however. So I just installed that, then I grabbed MATE and MintMenu from the repos, logged out, logged into a Mate session, and added the Mint Menu to the panel. Removed the default menus, moved Mint Menu to the side, and the result was about what you'd get if LMDE Mate/Cinnamon had installed properly.
Update: I was able to get the MATE/Cinnamon 64-bit version to install cleanly by running the image from a DVD instead of USB. It's my understanding that Unetbootin
can properly install the image to a USB stick, but I haven't yet confirmed. It's not an ideal solution, since Unetbootin apparently doesn't handle multiple Live CD images, unlike Multisystem or YUMI.