my @type = grep /\b$_\b/, @{$ACTUAL_TEAMS{$group}}
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This will always be true, because in the grep, $_ equals the active element -- you've written a tautology. Perhaps you mean:

#!/usr/bin/env perl
use strict;

my %ACTUAL_TEAMS;


my %TEAMS = (
    "NFL" => [ 'JETS', 'PATRIOTS', 'GIANTS', ],
    "MLB" => [ 'YANKEES', 'METS', 'CARDINALS', ],
    "NBA" => [ 'SIXERS', 'CELTICS','LAKERS', ],
);

while (<DATA>) {
        chomp;
        next if /^\s*$/ || /^\#/;
        my $aref = [split /,/, $_];
        push( @{$ACTUAL_TEAMS{$aref->[0]}}, $aref->[1]);
}


foreach my $group (keys %TEAMS) {
    #print "The members of $group are\n";
    foreach my $team (@{$TEAMS{$group}}) {
    #    print "\t$_\n";
print "MISSING:\tSPORT:$group\tTEAM:$team\n" unless (my @type = grep /
+\b$team\b/, @{$ACTUAL_TEAMS{$group}});
    }
}



__DATA__
NFL,JETS
NFL,PATRIOTS
MLB,YANKEES
MLB,CARDINALS
MLB,METS
NBA,SIXERS
NBA,CELTICS
NBA,LAKERS
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