Just Google worst auto-tune for examples, because it's so common now, most people don't notice it. Here's a list of some examples:
http://www.hometracked.com/2008/02/05/auto-tune-abuse-in-pop...
Also, if you're not really musical you might have a hard time picking it out. I found that as soon as I learnt an instrument, songs suddenly became layered and I could pick out and distinguish different instruments, and notice mistakes.
It seems to be more about recognizing the small glitches, rather than something involving overtones, which I would really have liked to learn more about how to recognize them. I have long found that autotuned singing sounds a bit more "metallic" to me.
Thanks anyway, the sound samples are useful in recognizing it better.