I assume "The Clapper" uses an analog high-pass filter plus some more filtering (analog or digital) to ignore continuous high-frequency sounds. The 2nd part is pretty-easy in software.
There's no way to absolutely-prevent false triggers, or misses if the clap is masked (drowned-out) by loud sounds.
Obviously, a clap has very-short duration so you can't have any delays while "listening" for the clap. Even without delays you can miss the peak of the clap because it only reads for an instant every time through the loop and the Arduino is rather slow. (I did some experiments once and it didn't miss the clap completely.) But I wasn't trying to do anything like what you're doing... I was just testing to see if a clap was too-short to "catch".