BMC001 is an easy build. You probably won't have any of these problems, but if you do, here are the causes a few of the most common problems and my recommended solutions.

1.It's out of tune!
Check your +5V supply. If you're running on less than 5V your quantizer's notes will seem flat, if it's higher they will seem sharp. If you're using an adjustable +5V supply, then adjust it until you're in tune. If you're using a 7805 on board regulator, swap it out for a different one. I buy the cheapest 7805s I can find and I've never gotten one so out of spec that it bothered my ears, you're probably going to get a good one. You can also use the 7805 to LM317 adaptor PCB to make a tiny adjustable +5V supply.

2.It sounds like the output is being modulated by a high frequency oscillator!
This is caused by one of three components being the wrong value: The 20mhz Crystal oscillator, the 10K resistor, or the .1UF cap that's connected to the 10k resistor. Make sure these are the correct values. The 20mhz crystal is controlling the frequency of the PWM output of the PIC, and the resistor and cap form a low-pass filter which filters this frequency out. If the crystal is too low a frequency, the PWM's frequency is too low to be filtered out by the low-pass filter. If the 10K and .1uf are wrong values the filter's cut off frequency becomes too high to filter out the PWM's frequency.

3.The output sounds slewed, note changes aren't crisp!
The low-pass filter on the output is set to too low of a frequency cut-off. This is caused by using a wrong value resistor or capacitor in the output filter.