I believe (looking at the module's documentation) that it expects individual lines to be passed as elements of arrays which you provide references to in text_diff. So, I think you need this:

#!/usr/bin/perl -w
use strict;
use Text::ParagraphDiff;

my $copy_old = qq|the first line
the second line is here
this really should be on separate lines, no?
weird eh?|;

my $copy_new = qq|the FIRST line
the second line is there not here
this really should be on sequential lines, no?
weird huh?|;

print text_diff([split /\n/,$copy_old], [split /\n/,$copy_new]);
[download]

Hope this helps