Your code has a number of problems:

• The first open call will, AFAIK, always fail because you are chdir()ed to the directory that contains the directory you've just found. So you're trying to write to a file with the same name as a directory. See the section about "the wanted() function" in the File::Find manpage.
• I don't thint the space in "> $dir" is a good idea - do ">$dir" instead.
• What is $file? You only use it once as far as I can see. This is where use warnings; can help you.

Anyway, none of this really helps you solve your problem. I would put the directory listings in a separate directory. Take a look at this code (untested):

use strict; 
use warnings; 
use File::Find;

my $listings_dir = 'c:/listings'; 

find(\&callback, 'c:/tmp'); 

sub callback { 
  my $file = $_; 
 
  # Check to see if $file is a directory
  if (-d $file) {
    # Get a list of all the files in the directory (inefficient)
    # (If you only want the filenames rather than paths as well, 
    # investigate using File::Basename. If you want just the files
    # in a directory, and directories within the directory, 
    # consider putting grep { -f $_ } before the glob. 
    my (@files) = glob($File::Find::dir . "/$_/*"); 

    # Save this list to a file
    open LISTING, ">$listings_dir/list$_.txt"; 
    print LISTING join ("\n", @files); 
    close LISTING; 
  }
}
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There is nothing wrong with open(FH, "> $file");

perldoc -f open says:

The filename passed to 2-argument (or 1-argument) form of open() will have leading and trailing whitespace deleted

I prefer to put some whitespace between the permissions operator and the filename, others do not. It's a style thing, but there is nothing wrong with it.

Preferably use warnings instead of perl -w. There is a thread here explaining why, but I can't track it down right now. See perldoc perllexwarn for more info.
You should consider using the strict pragma as well as the warnings pragma.

Another minor point - I personally find

my $dir = $entry;
open(FILE, "> $dir") or die "Can't open file, $dir: $!";
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slightly grating.
It's a file you want to create - I initially couldn't figure out if you really wanted opendir to open a directory handle, or if you wanted:

my $file = $entry;
open(FILE, "> $file") or die "Can't open file, $file: $!";
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It's little things like that which make maintenance programmers go insane :-)

As another poster has already pointed out, you can't go creating files, directories, pipes etc, in the same directory with the same name as an existing file/dir/pipe.

---

If the information in this post is inaccurate, or just plain wrong, don't just downvote - please post explaining what's wrong.
That way everyone learns.

Sorry, $file is wrong.- correct:$entry. thank you for your help. to the other people: thank you, too.

Question 1: You cannot write to a file with the name of an existing directory. Possibly helpful could be an extention ".txt" to that file

$dir=$entry . ".txt";
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A good explanation how File::Find works could be found in spurperl's Beginners guide to File::Find