A very interesting idea. A lot of potential.
I think it will have limited accuracy until the circuit is improved a bit. in particular, a PC input is not designed for accuracy, so I think it needs an automated calibrate step to match the two channels. I would also like to see a differential amp across the component under test at least to give a 4 wire measurement.
I like the way they take fourier transforms to eliminate the effects of everything but the test frequency. That is nice. Since most new PCs can sample at 96KHz or higher, there is a chance it could work at 100/120Hz and 10KHz as well as 1KHz. With the right circuit, I am sure the range could be extended from the miserable 0.01uF to 100uF to a full 0.1pF to 10,000+ uF.
To test anything over 100uF, it will need an amplifier to boost the signal power from the computer.
Also to cope with notebooks that often only have a mono Mic in, it would be good if the input could switch between the two measured signals.
Richard.