Trying to save serialized string to SQL, but then i am having problems with unserializing it because of quotes.
Example, string is "te'st", after serialize we have
mysql_query("INSERT INTO `table`(`string`) VALUES ('" . serialize(array('iId' =>$aSqlResult['typeID'], 'sName' => mysql_real_escape_string($sScanResultLine))) . "')");
You should pass the data through the escape function after the serialization, not before - which is what you are doing now.
$serialized = mysql_real_escape_string(serialize($data));
Use a parameterised query with PDO or MySQLi and you can forget about the escaping altogether.