my $dbh = DBI->connect("um","","","mysql") ||
die "Could not connect: $DBI::errstr\n";

This should be:</>

my $dbh = DBI->connect("DBI:mysql:$host", $user, $pass) ||
    die "Could not connect: $DBI::errstr\n";
[download]

Your SQL statement needs to be a quoted string:

my $sth = 
  $dbh->prepare("INSERT into people (fornavn, efternavn, 
                                     cpr, adresse, zip, 
                                     city, tjenestested) 
                 values ($fornavn, $efternavn, $cpr, 
                         $adresse, $zip, $city,   
                         $tjenestested"));
[download]

And I'm willing to bet that some of those column values should be quoted - but not knowing your schema, I can't tell which ones.

Also, you should check the return code from all of your functions:

my $sth = 
  $dbh->prepare("INSERT into people (fornavn, efternavn, 
                                     cpr, adresse, zip, 
                                     city, tjenestested) 
                 values ($fornavn, $efternavn, $cpr, 
                         $adresse, $zip, $city,   
                         $tjenestested"))
  || die $dbh->errstr;

$sth->execute || die $dbh->errstr;
$sth->finish  || die $dbh->errstr;
[download]

--
<http://www.dave.org.uk>

"The first rule of Perl club is you don't talk about Perl club."