Is there a symbolic purpose to the ingredients in the witches' stew? They use some nasty-sounding items.

Yes there certainly is. Much of it has to do with Judao-Christian mythology and Elizabethan beliefs. I'll mention a few.

Fillet of a Fenny Snake- The old testament. That evil snake in the grass who tricks poor Eve into eating the apple.

A bunch of nocturnal animals- Newt/Frog/Bat. I guess they are evil because they hang out at night. Apperently evil things like ghosts had to high tail it in the day time.

Scale of Dragon, Tooth of Wolf- Both scary animals who like the dark!

Root of Hemlock digg'd i' the dark- Yes, it's not only evil poison but dug up in the dark as well!

Liver of Blaspheming Jew- Nothing like a bit of anti-Semitism to cheer an Elizabethan audience!

Those are just a few examples. Hope they help.