I have a copy of Kali on my USB stick. It boots well enough, but when I select any of the live options it does not work and takes me back to the same boot menu. There is an error but it flies by on the bottom left hand of the screen and I can't see it. However when I choose one of the installation options it hangs when it tries to detect the live CD medium ('failed to copy file from CD ROM').

A textual install gives the following errors during the beginning:

mounting /dev/sda1 on /media failed: invalid argument
umount: can't umount /media: invalid argument

And it tries for /sda2 and /sdc and /fda about twenty times, then takes me to the usual install screens where it hangs at the same CD ROM error as above.

Sounds like you might have a faulty copy you DID verify the MD5 right?... what method did you use to get Kali on your USB stick?
Personally, I prefer dd rather than using a GUI, but I'm an old curmudgeon and honestly, tend to do things "the hard way"