I copied a few lines of code from the net and got it to work in my own test environment. When I placed the software on the production server (linux PHP 4.1.2) - it only "almost" worked.
The problem was that it had lines with statements like:

mysql_insert_id();

where strange id's sometimes were returned !

Then, when I changed the code to:

mysql_insert_id($con); // The ?resource link_identifier?

everything was fine. I believe that what happened was that my program received id's from somebody else doing INSERT on the same server?

My conclusion was:

Never use the function without the 
"resource link_identifier" !

And then again, - Why should you?

In the documentation it says:"If link_identifier isn't specified, the last opened link is assumed."

My code was simply:

$sql= "INSERT INTO xrefs  (referrer) VALUES ('$ref')";
echo "sql $sql <br>";
$result = mysql_query($sql,$con);
//$referrer_id = mysql_insert_id();  // FAILED
$referrer_id = mysql_insert_id($con); // WORKED OK