1. Bought superglue (the GEL kind, not the liquid), put a dab of it on the end of a toothpick, stuck the toothpick in there and let it sit half an hour. Just pulled it out, and the broken off end of the headphone plug came out with the toothpick perfectly. (It came out so easily, in fact, that I didn't realize it had worked until I looked down at the toothpick and saw the plug still stuck onto it.)
2. Proceed with caution...
3. I think the problem with using glue or indeed a magnet is that the jack plug and socket is designed to prevent the plug being removed with very little force. If it was sitting loosely enough to be pulled out with a drop of supergle on a pin or even a magnet, then it would probably be loose enough to fall out if you tipped the device on its side. Ever wondered why your iPod / iRiver / Discman headphones don't fall out constantly? Look at the shape of a jack plug. The shape of the socket mirrors this, so that it gently "latches" when inserted fully.
4. I think the chances of getting it out with glue are slim-to-none. This is a hole 3.5mm in diameter. Even if you can get a pin or paperclip down onto the broken piece of plug, there won't be enough surface area or glue to obtain a safe bond. And even if it did bond - the gentle "locking" mechanism of the jack socket would probably foil a tiny bond even with the strongest epoxy. If you tried to use more glue, you'd probably end up with a ruined jack socket, and a hefty repair bill.
5. Without a solid anchor on the piece that is inside the socket, I'd say that opening it up is the only real option. Or, if you're not prepared to do it, getting someone else to do it. The jack socket itself is an incredibly simple design, and once it's exposed you could simply push the end of the plug back out.
6. The hard drive is actually right next to the headphone jack, so it is a good thing you didn't use a more powerful magnet.
7. Like I said before, with a really fast drill, like a Dremel, you will be able to make a hole in the broken plug into which you can either force a small screw OR superglue a piece of piano wire and use that to pull the piece out. No, the plug will not rotate since the bit is spinning too fast; however, you have to have a lot of patience and drill in slowly, hence my suggestion of asking an experienced model builder or similar hobbyist. Could I do it? Yes, I have handled problems like this before. Only problem is that I live in another country many thousands of miles away.
8. It's probably a good idea to take the battery out anyway, to be sure the computer is off and you don't short something.
9. This is a mechanical problem, insertion of the plug physically disconnects the computer's output from the internal speakers.
10. If you have a friend who is into scale models, R/C planes or stuff and has the tools (like a Dremel rotary tool), they can try to drill into the stuck plug, force a small screw into the hole and use that to pull the piece out. If no such friend can be found, maybe you can take the Mac to a hobby shop and have them take a look.
11. I would have her find someone, like a jeweler, to try to extricate the remaining piece of the plug. If that fails, take it to someone who is familiar with laptop computers and can lookup the take-a-part manual on the internet.
12. The dental pick suggestion is your best bet