G'day doubleqq,

Here's another way to do it. This solution only uses a single loop and pulls two elements at a time from the array (using splice). If a pair wasn't found, the second element (if it exists) is put back on the array for retesting on the next iteration.

#!/usr/bin/env perl -l

use strict;
use warnings;

my @labsets = qw{
    lab1_set1.txt lab1_set2.txt
    oops___should_not_be_in_this_list.txt
    lab2_set1.txt lab2_set2.txt
    lab3_set2.txt
    lab4_set1.txt
    lab99_set1.txt lab99_set2.txt
    lab100_set1.txts
    lab100_set2.txt
    lab101_set1.txt
    lab101_set2.txts
};

while (@labsets) {
    my ($set1, $set2) = splice @labsets, 0, 2;

    if ($set1 =~ /^(lab\d+_set)([12])\.txt$/) {
        if (! defined $set2) {
            print 'NOT PAIRED: ', $set1;
        }
        elsif ($2 == 1 && $set2 eq $1 . '2.txt') {
            print "PAIRED: $set1 and $set2";
        }
        else {
            print 'NOT PAIRED: ', $set1;
            unshift @labsets, $set2;
        }
    }
    else {
        print 'BAD FILENAME: ', $set1;
        unshift @labsets, $set2 if defined $set2;
    } 
}
[download]

Output:

PAIRED: lab1_set1.txt and lab1_set2.txt
BAD FILENAME: oops___should_not_be_in_this_list.txt
PAIRED: lab2_set1.txt and lab2_set2.txt
NOT PAIRED: lab3_set2.txt
NOT PAIRED: lab4_set1.txt
PAIRED: lab99_set1.txt and lab99_set2.txt
BAD FILENAME: lab100_set1.txts
NOT PAIRED: lab100_set2.txt
NOT PAIRED: lab101_set1.txt
BAD FILENAME: lab101_set2.txts
[download]

Update: Made some changes to the code and added some additional tests. Old code (and old output) in spoiler below.