• You should verify that chdir worked.


• You create the variables $a1 $a2 $a3 $a4 $b1 $b2 $b3 $b4 but you never use them.


• You log a message if $current_ip could not be obtained but you proceed to the next step as if it had been.


• You log a message if "myip.txt" could not be opened but you proceed to the next step as if it had been.


• You compare the two strings $readip and $current_ip which may have extraneous trailing whitespace.


• Your use of system sends an error message to the log file when it succeeds but no message if it fails.

Something like this may be better:

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

use Tie::File;
use LWP::Simple;
use Sys::Syslog qw( :DEFAULT setlogsock );

my $file     = '/root/script/myip.txt';
my $emailadd = 'your@email.com';
my $fromadd  = 'ipwatch@yourmachine'; 


my $current_ip = get( 'http://www.chisono.it/ip.asp' ) or do {
    logit( 'err', "Cannot retrieve the IP address\n" ); 
    exit 1;
    };
$current_ip =~ s/\s+$//;

tie my @read_ip, 'Tie::File', $file or do {
    logit( 'err', "Cannot open $file: $!\n" );
    exit 2;
    };
 
if ( $read_ip[ 0 ] eq $current_ip ) {
    logit( 'info', "Address not changed\n" );
    exit 0;
    }

logit( 'info', "Address changed: old IP: $read_ip[0] ; New IP: $curren
+t_ip\n" );

$read_ip[ 0 ] = $current_ip;
untie @read_ip;

# 0 == system qq(mailx -s "IP changed!" -a "From: IPWatch <$fromadd>" 
+$emailadd < myip.txt) or do {
#
# Update -- changed "< myip.txt" to "< $file"
#
0 == system qq(mailx -s "IP changed!" -a "From: IPWatch <$fromadd>" $e
+mailadd < $file) or do {
    logit( 'err', "Cannot send the email!\n" );
    exit 3;
    };


sub logit {
    my ( $priority, $msg ) = @_;
    return unless $priority =~ /^(?:info|err|debug)$/;
    setlogsock( 'unix' );
    openlog( $0, 'pid,cons', 'user' );
    syslog( $priority, $msg );
    closelog();
    }
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