The zeroth parameter of a shell command is the command itself (or sometimes the shell itself). You should be using $1
.
(("$#" < 1)) && ( (("$1" != 1)) || (("$1" -ne 0q)) )
Your boolean logic is also a bit confused:
(( "$#" < 1 && # If the number of arguments is less than one…
"$1" != 1 || "$1" -ne 0)) # …how can the first argument possibly be 1 or 0?
This is probably what you want:
(( "$#" )) && (( $1 == 1 || $1 == 0 )) # If true, there is at least one argument and its value is 0 or 1