Yet another way to do it:

#!perl

use strict;
use warnings;

my @sets =
    ([ 0, 1, 2, 3,          7, 8, 9, 10, 11, 12, 13, 14, 15,     ],
     [ 0,       3,          7, 8,    10, 11,     13, 14,     16, ],
     [ 0, 1, 2, 3,    5,    7, 8,    10, 11, 12, 13, 14,     16, ],
     [       2, 3, 4,    6, 7, 8,    10, 11, 12,     14,     16, ],
     [ 0, 1, 2, 3,          7, 8, 9, 10, 11,     13, 14, 15,     ]);

my @intersection;

print join("\n", map(join("  ", @$_), @sets)), "\n\n";

while (@sets == grep {@$_ > 0} @sets) {
    @sets = sort {$a->[0] <=> $b->[0]} @sets;
    if ($sets[0]->[0] == $sets[-1]->[0]) {
        push(@intersection, $sets[0]->[0]);
        shift(@$_) for @sets;
    } else {
        my @ne = grep {$sets[0]->[0] != $_->[0]} @sets;
        my @eq = grep {$sets[0]->[0] == $_->[0]} @sets;
        shift(@$_) for @eq;
        @sets = (@eq, @ne);
    }
}

print join("  ", @intersection), "\n";
[download]

Just my 2 cents, -gjb-