And a quick cleanup:

#!/usr/bin/perl
use warnings;
use strict;
use Getopt::Long;
use Pod::Usage;

#********************************************************
#**  Process command line arguments.
#********************************************************

GetOptions(
    'add=s'  =>\my $Add_Record,
    'edit=s' =>\my $Edit_Record,
    'list=s' =>\my $List_Records,
    'view=s' =>\my $View_Record,
    'man'    => sub {pod2usage({-verbose => 2, -input => \*DATA})},
    'help|?' => sub {pod2usage({-verbose => 1, -input => \*DATA})},
);

if (($Add_Record xor $Edit_Record) xor ($List_Records xor $View_Record
+))
{
# Run Program
}
else
{
#  Print manual
}

__END__

=head1 NAME

somescript -- A utility for ...

=head1 SYNOPSIS

B<somescript --help> for more information

    somescript [options]

Options:
[download]

Note a few things.

• First, the short forms of the options are automatically available. You don't need to add them.
• Taking a reference to a variable when you declare it is a nice shorthand.
• I have pod2usage take __DATA__ as the input because I've had problems with this working when I do funky things with directories.