• "$filename"
  doesn't need to be in quotes.
  $filename
  will do fine.

• open INFILE, '<', $filename
  is less error-prone and safer than the two-arg version.

• It's good to use local variables for file handles. Replace
  open INFILE, '<', $filename
  with
  open local *INFILE, '<', $filename
  or
  open my $fh_in, '<', $filename

• open local *INFILE, '<', $filename || die "cant open the input file";
  is the same as
  open local *INFILE, '<', ($filename || die "cant open the input file");
  which is definitely not what you want. Use
  open(local *INFILE, '<', $filename) || die("Unable to open the input file: $!\n");
  or
  open local *INFILE, '<', $filename or die "Unable to open the input file: $!\n";

• We don't need to know how many # and * we have in a row, so
  if (/[\#\*]+/)
  can be simplified to
  if (/[\#\*]/)
  And since # and * are not special in character class, you don't need to escape them. The following in sufficient.
  if (/[#*]/)
  Also, the parens are optional on a if suffix, and just add clutter in this case. I'd remove them as follows:
  if /[#*]/

• I think "to filter out lines" means "to remove lines". If so, replace
  if /[#*]/
  with
  unless /[#*]/

• Your print is adding spaces. Replace
  print "@filtered";
  with
  print @filtered;

We get the following:

open(local *INFILE, '<', $filename)
   or die("Unable to open the input file: $!\n");

my @filtered;
while (<INFILE>) {
    push(@filtered, $_) unless /[#*]/;
}

print @filtered;
[download]

What follows is a more elegant but more memory intensive alternative:

open(local *INFILE, '<', $filename)
   or die("Unable to open the input file: $!\n");

my @filtered = grep { !/[#*]/ } <INFILE>;

print @filtered;
[download]