Also, you could change your verification code to be somewhat more like this:

#!/usr/bin/perl

use strict;
use warnings;
use v5.10;

sub edit_file {
    my $my_file = shift;
    my $editor = $ENV{'EDITOR'} || 'vim';
    system($editor, $my_file);
}

sub validate_file {
    my ($my_file) = @_;
    my $error;

    open(MY_FILE, '<', $my_file) or die "Unable to open file [$my_file
+]: $!";
    while(<MY_FILE>) {
        chomp;
        given ($_) {
            print("Checking [$_]\n");
            if (/^[^[:lower:]]/) { # Line does not start with a lowerc
+ase letter
                $error = "$_ does not begin with a lower case letter";
            }
            if (/somethingorother/) {
                $error = "$_ has somethingorother";
            }
            default {
                # Line is ok
            }
        }
        if ($error) {
            $error = "At line [$.]: $error";
            close( MY_FILE );
            return $error; # Stop parsing the file after the first err
+or
        }
    }
    close(MY_FILE);
    return undef;
}

my $string = join( "\n", qw(howdy partner goodbye Friend saynora adios
+ Amigo) );
open(MY_FILE, '>', 'my_file.txt') or die "Can not open my_file.txt: $!
+";
print MY_FILE $string;
close(MY_FILE);
edit_file('my_file.txt');

my $error = 'Nothing went wrong';
while ($error) {
    $error = validate_file('my_file.txt');
    if ($error) {
        print "Error validating file: $error\n";
        print "Hit return to continue: ";
        <STDIN>;
        edit_file('my_file.txt');
    }
}
print "File is ok\n";
[download]

This uses a given-when construct to allow you to easily add more checks. It also incorporates some of the suggestions mentioned by other monks.
The validation-loop has been moved out of validate_file and the returnvalue of validate_file has been used in a more descriptive matter.
Note that this relies on the truth and falsehood of the empty string (undef is false, empty string is false, nonempty string is true).

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