Put the return value from ls into a variable, and filter the file names for the extensions you want to allow. It's better to do it this way than filtering through ls, imho.

EDIT: Here's some code:

#!/usr/local/bin/perl

use strict;
use warnings;

my $base = '/u/web/user/';
my @allow = qw/log txt sql err par csv/;
my $e;

print "Content-type: text/plain\n\n";
for (split /\n/, `ls -lt $base`) {
    for $e (@allow) {
        if (m/\.$e$/) {
            print "$_\n"; last;
        }
    }
}
[download]

The advantage of doing it this way is that your code is easy to modify to work with rejected lines, should you decide you want to in the future.