sub new {
   my $class = shift;
   my $id    = shift;
   my $self  = {
      _ID        => $id,
      _FINALIZED => 0,
      _EXPENSES  => [],
      _TOTAL     => undef,
      _COUNT     => undef,
   };
   return bless $self, $class;
}
[download]

• in ExpenseReport::add_expense() -

  $newexp->{_ID} = $#expenses + 1;
  [download]

  seems more intuitive as

  $newexp->{_ID} = scalar @expenses;
  [download]

• in ExpenseReport::save_file - get rid of the temp variable and just use

  local $Data::Dumper::Indent = 3;
  [download]

  You are doing that in ExpenseReport::finalize, so i suspect this code was overlooked.
• ExpenseReport::load_file() - try this instead

  # open file
  my $file = do {local $/; <REPORT>};
  [download]

• I notice that you connect, disconnect, and reconnect several times to the database - this may be desired behavior, but consider opening a connection and saving it as an attribute of the class, or as another class.
• Inside ExpenseReport::finalized() and all of Expense's methods - change those one line if's to:

  $self->{$hiddenkey} = shift if @_;
  [download]

Over all, very good work. And good luck with the next step. :)

jeffa

L-LL-L--L-LL-L--L-LL-L--
-R--R-RR-R--R-RR-R--R-RR
B--B--B--B--B--B--B--B--
H---H---H---H---H---H---
(the triplet paradiddle with high-hat)