I saw the latest email about rust updates, so I installed and ran rustup. It said I had to delete my old version, so I did. Next rustup failed for permissions on ~/.cargo/bin, but I fixed that problem with chmod (sudo didn't work???). Following the successful install, I got
Everything you describe here sounds strange! I don't recall which situation rustup asks the user to delete rustup before upgrading. I think it probably insists on system installs of rust being uninstalled first, or multirust.sh being uninstalled first though.
Some of this could be fallout from the transition from using the ~/.multirust directory to ~/.rustup - e.g. your eclipse plugin may be aware of the former but not the latter, though rustup is supposed to maintain ~/.multirust as a symlink to ~/.rustup.
~/.cargo/bin being unwritable is indicative of something weird. Maybe an old system/multirust install where cargo install was previously run under sudo.
I don't know what the "couldn't prepare build directories" error means, but it sounds suspiciously like a directory with the wrong permissions.
The PATH should include ~/.cargo/bin. rustup should configure this, but is known to be buggy about it.
To get rustup working again, you might delete ~/.multirust, ~/.rustup, and ~/.cargo (the three of which contain all of the rust installation), and do a fresh install. If that doesn't result in a working rust I would be surprised again.
I don't know anything about the eclipse plugin but imagine it is either just reflecting the busted rust installation, or needs to be updated for compatibility with current rustup.