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.
I've played piano and sung for most of my life, but I wouldn't have recognized many of these if you hadn't pointed them out, though I do recognize many structures and mistakes in music.
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.