Classical piano and human voice are the biggest challenges for any audio system to reproduce correctly.
I have to go along with this, too. The piano raises a number of challenges. The dynamics between the moment just before the hammer hits the string and the moment of impact, for instance, is a huge leap in dynamics. But it's not just about capturing and playing back that impact. The notes bloom out and then decay. It's a fairly complex sound when it's just one key, but throw in whole chords comprised of two or more of these interactions between string and hammer, and you have a very complex audio signature. Consider, too, the subtleties and nuances that comprise a great deal of a classical pianist's performance. It's not just about being loud or soft, but the artist really has to know the instrument, and they're doing things with their hands and feet and the keys and pedals to coax out a very particular sound.
While it's true that all musical artists are doing the same thing, there's just something about a classical piano piece that's really hard to get right in the playback mode.
The human voice, because we all know it so well. That familiarity with how the voice sounds, or should sound, is, as someone intimated in an earlier post, just makes reproducing the sound in a way that will fool the listener into believing that it is, in fact, the human voice and not a reproduction, an incredible engineering challenge. But that's not all... there's all the mechanics going on inside our mouths that make a vocal sound... the shape of the lips and tongue, the position of the jaw, and all those goofy things that speech therapists like to talk about are being reproduced by a device that's simpler than the human mouth by several orders of magnitude.
I have a copy of this great demo disk (CD) that B&W provides its dealers. It features recordings mastered at Abbey Road (because they use B&W speakers as their studio monitors), and there's a recording of Peggy Lee singing Fever (yes, I know, the recording was made well before B&W existed... my guess is that it was re-mastered at Abbey Road, but I can't say for sure), and you can really get a feel for her mouth's presence around the microphone. It's crazy.
So those are my reasons for why I think the piano, more specifically classical piano, and the human voice are the biggest challenges for audio systems.