First of all, don't add mint repositories to Debian, not a good idea. Mint is based on Ubuntu which, while based on Debian, is not 100% compatible with Debian repositories. Mixing them is likely to cause trouble. Instead, add LMDE (Linux Mint Debian Edition) repositories. LMDE is Debian and is 100% compatible with the Debian repos. As long as you're running Debian testing, that should work with no problems.
Second, as others have pointed out, this is really truly not worth the effort.
Anyway, the error you get is actually
run-mozilla.sh: Cannot execute .
. is important, it shows that the script expects an argument and since you don't give it one, it takes the current directory. The script is not an installer and is usually called by another script, not directly.
To install the thunderbird binaries, follow the instructions here:
wget 'http://releases.mozilla.org/pub/mozilla.org/thunderbird/releases/3.1.4/linux-i686/en-US/thunderbird-3.1.4.tar.bz2 -O- | ' sudo tar xj -C /opt && sudo ln -s /opt/thunderbird/thunderbird /usr/bin/thunderbird
However, this will install the 32bit thunderbird which won't work on a 64bit system unless you have multiarch installed. You will also need to bring in the dependencies manually. Please don't do this, either install the deb from LMDE or just use icedove which is thunderbird with different icons.