Some parts within a Performance seem to be interacting with other parts of the same Performance even though these parts are set to different MIDI channels. In addition each part sounds fine in isolation.

This is usually due to the portamento function. Portamento should only
be applied to a monophonic program / part. The Supernova / Nova will
let portamento be applied to a polyphonic program in the Program mode
and this will have repeatable results even though this is not standard
practise. If a polyphonic part within a Perfomance has a level of
portamento assigned to it, this will have repeatable results if this
part is played in isolation. If another part is played simultaneously,
even on a different MIDI channel this will not give repeatable results.
This is because the Supernova and Nova allocate voices dynamically.

The portamento effect is used to glide between two adjacent voices. In
Performance mode these voices cannot be distinguished between parts
hence the portamento can very easily glide between a voice from one
part and the next sounding voice which may be from a different part.
The solution is to either set the portamento value to 000 or to change
the polyphony of the part with the portamento effect to "mono".