For example, if one key has two check ins or two check outs in a row, it would be flagged. I'm really not sure how to do this. Any ideas?

It looks likely your table structure is not ideal but if you are stuck with it you can use user defined variables to hold previous record values

SELECT key_number, dateadded,
  IF (action=@last_action AND key_number=@last_key,"ERROR","OK"), 
  @last_action := action, @last_key := key_number
  FROM ( SELECT *
    FROM keysafe
    ORDER BY key_number, dateadded
  ) as x
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Initialise the variables before use with

$dbh->do('SET @last_action := "UNKNOWN",@last_key="UNKNOWN"');
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alternatively use perl variables

my $sql = 'SELECT key_number,action,dateadded
           FROM keysafe
           ORDER BY key_number, dateadded';
my $sth = $dbh->prepare($sql);
$sth->execute();
my ($last_key,$last_action);
while (my ($key,$action,$date) = $sth->fetchrow_array){
  my $status = 'OK';
  if (($key eq $last_key) && ($action eq $last_action)){
    $status = 'ERROR';
  };
  print "$key,$action,$date,$status\n";
  $last_key    = $key;
  $last_action = $action;
}
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poj