The error I kept getting was :
./firefox-bin: error while loading shared libraries: libmozjs.so: cannot open shared object file: No such file or directory
I also got :
./firefox-bin: error while loading shared libraries: libstdc++.so.5: cannot open shared object file: No such file or directory
A quick search shows that most of the files missing live in :
/home/me/firefox
/usr/lib/iceweasel
Of the possible solutions this is the one that worked for me. I know it's not the prettiest fix but it will due.
1. Download and unzip Firefox.
2. apt-get install libstdc++5
3. Copy the libs from /home/you/Firefox/ to /usr/lib/ (or some other acceptable place).
4. Run firefox-bin from the directory you unzipped it in.
Other possible solutions :
Add /home/you/Firefox to your path
Create symbolic links from the libs in /Firefox/ to /usr/lib (or something)
Other files Firefox may complain about being missing :
libfreebl3.so
libnspr4.so
libnss3.so
libmozjs.so
libnssckbi.so
libplc4.so
libplds4.so
libsmime3.so
libsoftokn3.so
libssl3.so
libxpcom_compat.so
libxpcom_core.so
libxpcom.so
libxpistub.so