I don't like the regexp approach for this type of problems, I find it easier to dissect things one by one...

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

sub ipverify
{
    my( $ip ) = @_;

    if($ip =~ /[^\d.]/) {
        die "Found illegal characters in ip: $ip";
    }
    my @octets = split( /\./, $ip );
    if(@octets != 4) {
        die "number of octets must be 4";
    }

    foreach my $octet (@octets) {
        ## numerical sanity
        if($octet < 0 || $octet > 255) {
            die "octet $octet is out of range ( 0 <= x <= 255 )";
        }

        ## $octet should not start with a 0 if it evaluates to
        ## less than 100
        if( $octet < 100 ) {
            ## if 0, octet should be single digit
            if($octet == 0 && length($octet) != 1) {
                die "bad representation '$octet'. rewrite as '0'";
            }
            if($octet =~ /^0+(\d+)$/) {
                die "bad representation '$octet'. rewrite as '$1'";
            }
        }
    }
    return 1;
}

sub hostname_verify
{
    my($hostname) = @_;
    my $iaddr = gethostbyname($hostname);
    if(!$iaddr) {
        die "Hostname '$hostname' did not resolve";
    }
    return 1;
}

sub main
{   
    while(1) {
        print "Type in IP address or hostname to verify (enter to quit
+): ";

        chomp(my $input = <STDIN>);
        if(!length($input)) {
            last;
        }

        if($input =~ /\D/) {
            eval{ hostname_verify($input) };
        } else {
            eval{ ip_verify($input) };
        }
        if($@) {
            (my $err = $@) =~ s/ at .*$//;
            print STDERR "   ERROR: $err\n";
        } else {
            print "$input is a valid address\n";
        }
    }
}

main();
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