I'm curious to what makes something qualify as a ground?
Ground is some universal conductor having potential being shared between entities. If you stand nearby another person, you share literal ground with him or her. If you connect two circuits, they must know what their grounds are so that they qualify signals between them properly.
So here we come that you need to not only consider ground, but ground in couple with another conductor which makes potential, electrons moving, and thus electrical current, and thus make circuits work.
chassis of the car is used as ground because it's such a big metal piece
It is referred as ground because other entities, including driver, share it.
Therefore it's a 'zero potential'.
Potential is relative. To have potential you need another wire.
But how big does the metal object have to be, compared to the (e.g.) battery it's connected to.
It must not be big, it mist be accessible. There're circuits which have negative wire as ground, some have positive wire as ground.
what makes the metal object qualify as a ground?
Designer of the electronic device, and regulating authorities (safety and legal documentation).
Well, what is a ground, and what is not?
There're special symbols for ground in circuit design; if you do not have circuit or unsure, it would be fairly logical to ask: "where is the ground?" :)