For fun, I did a rewrite. I haven't tested it, but it compiles cleanly.

my $dir = "/Path/to/a/data/directory";
my %hash;
$hash{$_} = hashify_file( $_ ) for ls_dir( $dir );

sub ls_dir {
    my $dir = shift;

    opendir my $dh, $dir
        or die "Can't opendir '$dir': $!\n";

    return map  { "$dir/$_" }
           grep { !/^\./ && !/\~$/ } readdir $dh;
}

sub hashify_file {
    my $file = shift;

    open my $fh, '<', $file
        or die "Can't read '$file': $!\n";

    my $out;
    %{$out} = ( %{$out}, %{hashify_line( $_ )} ) for <$fh>;

    close $fh or die "Can't close '$file': $!\n";

    return $out;
}

sub hashify_line {
    my $line = shift;

    chomp $line;
    $line =~ s/^\s+//;
    return {} if ( $line =~ /^\#/ || $line =~ /^\s*$/ );
    my ( $key, @values ) = split /\t/, $line;

    return { $key => \@values };
}
[download]

As to your question, I think a grep on readdir would be the best way to go to get your list of files. The files themselves, you could process line-by-line instead of reading every line at once, and that might be better.

You might be able to get the shell to do even more of the work for you, though.

my $dir = "/Path/to/a/data/directory";
my %hash;

open my $grep_fh, '-|', "grep '^' $dir/* /dev/null"
    or die "Can't grep: $!\n";
while ( my $line = <$grep_fh> ) {
    $line =~ s/^([^:])://;
    my $file = $1;
    next if $file =~ /\~$/;
    %{$hash{$file}} = (%{$hash{$file}}, %{hashify_line( $line )});
}
close $grep_fh or die "Error closing grep pipe: $!\n";
[download]

This way, you get grep and the shell to do all the I/O.

Notes:

• I hope you don't have any filenames with a colon in them.
• This uses sub hashify_line as defined in the <readmore> above. (Hey, refactoring pays off!)
• We assume also that $dir does not contain any shell metacharacters. If yours isn't really a literal as in your example, you may have to sanitize it.
• You could probably get grep to do some of your line filtering for you, but I'd just as soon do that in Perl.
• Likewise, you could use find and xargs to choose the file list to pass to grep, and I'd really rather do that in Perl.
• Both of those "rather do that in Perl" statements may need to be reevaluated in light of performance problems. (For example, if you waste a lot of time ignoring lines.)

Update: broomduster makes a good point in Re: greater efficiency required (ls, glob, or readdir?) also. If you have too many files, the "$dir/*" to the shell is going to bomb. Time for xargs, then. Something like:

my $cmd = "find $dir -type f -print | xargs grep '^' /dev/null";
open my $grep_fh, '-|', $cmd
    or die "Can't grep: $!\n";
[download]

Then you may have to filter out dot files somewhere.