Did you print your query to the screen to see just what you ware trying to do?
cahnge your code to this:
$query="update arrangement set dato='$dato' and navn='$arrnavn' and
ArrangementKategori='$kategori' and entre='$entre' and AntalPersoner='$antal' where id='$id'";
print $query;
if (!($res=mysql_query($query)))
{
echo mysql_errno().": ".mysql_error()."<BR>";
};