From perldoc -f vec it says:

vec EXPR,OFFSET,BITS
        Treats the string in EXPR as a bit vector made up of elements 
+of
        width BITS, and returns the value of the element specified by
        OFFSET as an unsigned integer.
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You're doing nasty stuff with references to variable names, which would flail with use warnings so you code like this at your own peril.

First, line 16, change from

    for (@{$domains[$i]}) { vec($scratch,$_,1) = 1}
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to

    for (@{$domains[$i]}) { vec($$scratch,$_,1) = 1}
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Next, the ending for loop, should written as follows:

for ( $j = 0; $j <= 5; $j++ )
{
    my $scratch = "domains$j";
    for ( $i = -100 ; $i <= 2000 ; $i++ ) {
    if (vec($$scratch,$i,1)){
        print "\t $i recognised as part of the 1st domain using the ne
+w method\n";
        }
    }
}
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Note the second for loop, and the use of the scratch variable.

I would never personally code like this, but hopefully it is of some assistance to you.

Update: fixed a mis typed code tag.