A few things are happening in your code:
1) You have little insert pieces throughout your code. There really is not need for this, and it makes debugging & understanding your scipts later on really hard. Better try to do all the manipulation stuff in one location, and create the output in another. I racked all the php together so i can post it here. You should do this in your code too, and remove all <?php ?> tags from the rest of your code.
2) For the first insert you do not test whether the form was actualy submitted. So both upon loading the form, as with inserting the form data gets inserted. That is what was bugging you. See code below.
3) For formatig the form you should not be using all the font, strong etc tags, but you should be using Cascading Style Sheets, or CSS. The way you code it now is very big and lumpy in download
// IF you have multiple files, you should place the login details in a separate file, and include it if you need database activity on a page
// Make sure you verify the submitted data, and do basic anti-sql inject stuff
// such as mysql_escape_real_string()
$RNo=$_POST['Report_No'];
$NVessel=$_POST['Name_of_Vessel'];
$RTime=$_POST['Report_Time'];
$DAccident=$_POST['Date_of_Accident'];
$TAccident=$_POST['Time_of_Accident'];
$IPName=$_POST['IP_Name'];
$IPSname=$_POST['IP_Surname'];
$IPDOB=$_POST['IP_DOB'];
$IPNat=$_POST['IP_Nationality'];
$IPsex=$_POST['IP_Sex'];
$IPSAdd=$_POST['IP_Address'];
$IPPass=$_POST['IP_Passport'];
$DOEvent=$_POST['Desc_of_Event'];
// HERE you should have tested whether dtaa was actualy posted.
$query="INSERT INTO Report(
Report_No, Name_of_Vessel, Report_Time, Date_of_Accident, Time_of_Accident, IP_Name, IP_Surname, IP_DOB,
IP_Nationality, IP_Sex, IP_Address, IP_Passport, Desc_of_Event) VALUES ('$RNo','$NVessel', '$RTime','$DAccident',
'$TAccident','$IPName', '$IPSname','$IPDOB', '$IPNat',
'$IPsex','$IPAdd','$IPPass', '$DOEvent')";
$result=mysql_query($query)
or die( "There was an error running '$query' " . mysql_error());
if(isset($_POST['Location']))
{
$values = implode(",", $_POST['Location']);
$query = "INSERT INTO const_location (Location) VALUES('$values')";
mysql_query($query) or die("Error inserting into const_location: ".mysql_error());
}
mysql_close($connect);
if(isset($_POST['Type']))
{
$values = implode(",", $_POST['Type']);
$query = "INSERT INTO const_acc (Type) VALUES('$values')";
mysql_query($query) or die("Error inserting into const_acc: ".mysql_error());
}
if(isset($_POST['Injured_person']))
{
$values = implode(",", $_POST['Injured_person']);
$query = "INSERT INTO position (Injured_person) VALUES('$values')";
mysql_query($query) or die("Error inserting into position: ".mysql_error());
}
?>