First off, I think this is a solid application. Well done!
Here are some ideas:
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Some key buttons could be larger, such as the pitch adjust buttons. They are too closely spaced and too small.
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I find the cross fader partially effective. What I would suggest if a mode where you can use the full screen real-estate to fade on the x-axis between tracks, and assign along the y-axis a filter or effect (it could actually just increase the effect bus). Not sure if Korg would rule a patent in this area though.
It would be great to have this feature, you could use multi-touch to perform certain mix tasks. For instance, you place you finger down on one side of the screen, so you can just hear one track, tapping a second finger down will cut to the other track. You could then drag your finger along the y-axis to create an effect.
You could design it so that placing a third finger down (so that two fingers are together) could activate another effect, such as a delay…
Also, in this expand mix screen, the background could still show the tracks and the time left.
Basically, I just think that there are better ways to use a touch interface than just emulating the hardware world.
I think the hardware metaphor is a great basis, and makes it approachable, but their is an opportunity to turn this into a new way to mix.