You are looping 8 times. You are printing it is new error before you check all possible elements. I have modified your code to fix this issue. Second part of the code is using a hash. It is much better way to check if elements are present.

#!/usr/bin/perl

use strict;
use warnings;

my @exerrors = (123,456);
my %adv79    = (123=>1,456=>1,789=>1,777=>1);
my $flag = 0;

foreach my $adv79key (keys %adv79) {
    $flag = 0;
    foreach my $exerrors (@exerrors) {
        if ($adv79key == $exerrors) {
            print "$adv79key is an old error\n";
            $flag = 1;
            last;

        }
    }
    print "$adv79key is a new error\n" if (0 == $flag);
}

print $/;

my %newerr   = map {$_ => 1} @exerrors;

foreach my $adv79key (keys %adv79) {
    if (exists($newerr{$adv79key})) {
        print "$adv79key is an old error\n";
    } else {
        print "$adv79key is an new error\n";
    }
}
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Output

456 is an old error
123 is an old error
789 is a new error
777 is a new error

456 is an old error
123 is an old error
789 is an new error
777 is an new error
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update: fixed typo