How can I move just one email within a conversation (a response from one person within a conversation for example) into a label/folder without moving the entire conversation?
You can't, really. When you're looking at the conversation it shows all the labels on all the messages.
The only way to really do that is to turn off conversation mode, but that's like using TNT to kill a fly.
One hack-y thing you could do is forward the message to yourself (and be sure to change the subject line). Then label that forwarded message as you like.
So far I have not found a way to do this, very annoying especially when I get emails with the same subject that I don't want to be threaded.
The only way I have found out how to do this is use an IMAP client (e.g. Mail app on iPhone) and then you can move any emails you like, threaded or not.