Not really. Subsequent studies show that the original experiment by Kettlewell was valid. I'm not an expert in this field but the scientific papers seem sound. http://rsbl.royalsocietypublishing.org/content/8/4/609

In any case, the peppered moth example is only an illustration of the idea of natural selection.

Peppered moths experiment is discredited: http://natureinstitute.org/pub/ic/ic8/moth.htm