Hiya routedude,
I added <code> tags around your example code, and tweaked some to make it clearer to my short-bus brain.   I found this syntax for matching-the-intersection-of-two-arrays on page 106 of The Perl Cookbook, and also moved the file opens/closes as close to each ofther as possible - always a good habit.
 
Anyways, I *think* this will do what you want or at least be close.   Wiser monks than I might show how to make it scale to more than just two days' acl log files.   The 'while... push unless /matches/' chunks could likely become a subroutine, but as is, this maybe shows some direction.
  cheers,
  ybiC
    striving toward Perl Adept
    (it's pronounced "why-bick")

#/usr/bin/perl -w
use strict;

# define output+input filenames:
my $outFile = 'aclLog.txt';
print "Enter filename that contains output of show access <list\n";
chomp my $aclMatchesDay2 = <STDIN>;
print "Enter the second file\n";
chomp my $aclMatchesDay2 = <STDIN>;


# check for no-matches in first input file:
open (ACLM1, $aclMatchesDay1) or die "Couldn't open $aclMatchesDay1: $
+!";
while (<ACLM1>){
  push @noMatchesDay1 unless /matches/;
}
close ACLM1 or die "Couldn't close $aclMatchesDay1: $!";


# check for no-matches in second input file:
open (ACLM2, $aclMatchesDay2) or die "Couldn't open $aclMatchesDay2: $
+!";
while (<ACLM2>){
  push @noMatchesDay2 unless /matches/;
}
close ACLM2 or die "Couldn't close $aclMatchesDay2: $!";


# check for overlap betwixt two input files:
my %isect;
foreach $e (@noMatchesDay1, @noMatchesDay2){
  $isect{$e}++;
}
my $noMatchesEver = keys %isect;


# print said overlap to output file:
open (OUT, ">>$outFile") or die "Couldn't open $outFile: $!";
print "$_\n" for @noMatchesEver;
close OUT or die "Couldn't close $$outFile: $!";
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