Try sending all errors to a file instead of the console.

Something like should do the trick:

BEGIN {
  $|++;
  open(STDERR, ">>", "mysterious_errors.txt");
}
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The >> is so that you append new errors to the file instead of overwriting it each time your program is run.

Also add error checking with something like:
do_something_with(@my_args) or die("Couldn't so_something_with ", $!);