if ( $today > $start && $today < $stop ) {
  if ( $today!= $notthisday[0] ) {            
    if ( $today != $notthisday[1] ) {              
      if ( $today != $notthisday[2] ) {                
        if ( $day == $dayofmon[0] || $day == $dayofmon[1] ) { 
          print "$today is the day.";
        }
      }
    }
  }
}
[download]

I'd have to kill you if you implemented this in my code base :)

The and-composite is much better and will not draw criticism. By any chance could you put a negated grep in there for the notthisday part to make it a little more Perlish? Also, add some parens rather than relying on your knowledge of the operators as a cautionary technique.

Halley's quick fail routine is one I like a lot, but I think kesterkester's technique may be better for more complex tests, to a C programmer, that's just extra code to read through (IMHO) -- yet allows you to reuse things at the price of method call overhead. But hey, if you are reusing things, you are better off using a really cool well-tested Date module!.