When you are using standard headphones, the only audio input available to SignalScope would be the built-in mic. However, the audio input is automatically selected by the iPhone, and sometimes when you connect headphones, the iPhone doesn't even select the built-in mic. In this case, no input channels show up, because there are none, and the time scales shows "nan" because the current sample rate is effectively zero. A zero sample rate would indicate an infinite sample period, which is where the divide-by-zero comes from. At this point, all we can do is improve the labeling to tell that user that no input device is selected.
I have successfully used the headphone output, with iPod touch earbuds and other adapter cables, simultaneously with the built-in mic. It seems to be a matter of plugging the headphones in at the right time so the iPhone will select the built-in mic as an input. You might want to try working with your iPhone headset and then switching to the headphones to see what happens.
Ben