Hi Chris, Thank you for the prompt reply! I created an example to demonstrate the issue. Here is the URL link on LiveSQL and I also pasted the script below (let me know if you can't access it)
https://livesql.oracle.com/apex/f?p=590:43:11624330239868::NO:RP:P43_ID:234570232171845590041795861264537934038&success_msg=TmV3IFNjcmlwdCAmcXVvdDtkYm1zX212aWV3LnJlZnJlc2hfZGVwZW5kZW50X3Rl.,c3QmcXVvdDsgc2F2ZWQgd2l0aCAxNSBzdGF0ZW1lbnRz%2Fj4436TyJMbt6IUlrrWbwPeYeqhdSAk0ZhLqENrcArSEdSlxhdUF-_DU5mKbaQu6YbHRRDTTWQMHVF948E9Yrvw


-- raw script
/*
1. DROP table and materialized View
2. Create table
3. Add two records with unique ID column values
4. Create materialized view
5. Add primary key to materialized view
6. Run dbms_mview.refresh_dependent with SUCCESS
7. Display materialized view data after first refresh
8. Add additional record to table with duplicate ID that would error the materialized view when refreshed
9. Refresh the materialized view for the second time
10. Error thrown but no value for "number_of_failures" (even when repeating the process multiple times)
*/
set serverout on
--set feedback off
--#1
DECLARE
mv_does_not_exist EXCEPTION;
PRAGMA EXCEPTION_INIT(mv_does_not_exist, -12003);
BEGIN
EXECUTE IMMEDIATE 'DROP MATERIALIZED VIEW MV_TABLE1';

EXCEPTION
WHEN mv_does_not_exist THEN
NULL;
END;
/
DECLARE
table_view_does_not_exist EXCEPTION;
PRAGMA EXCEPTION_INIT(table_view_does_not_exist, -942);
BEGIN
EXECUTE IMMEDIATE 'DROP TABLE T_SALARY CASCADE CONSTRAINTS PURGE';
EXCEPTION
WHEN table_view_does_not_exist THEN
NULL;
END;
/
--#2
CREATE TABLE t_salary (
id NUMBER,
salary NUMBER
);

--#3
INSERT INTO T_SALARY values(1,10000);
INSERT INTO T_SALARY values(2,20000);
COMMIT;

--#4
CREATE MATERIALIZED VIEW mv_table1 AS
SELECT *
FROM t_salary;
--#5
ALTER TABLE mv_table1 ADD CONSTRAINT pk_mv_table1 PRIMARY KEY ( id );
--#6
DECLARE
n_failures number;
BEGIN
dbms_output.put_line('Materialized view first refresh');
dbms_output.put_line('============== 111 =============');
dbms_mview.refresh_dependent(number_of_failures => n_failures,
list => 'MV_TABLE1'
,atomic_refresh => TRUE
,nested => TRUE
);
dbms_output.put_line('Number of failures: '||n_failures);
EXCEPTION
WHEN
OTHERS THEN
dbms_output.put_line('Error: '||SQLERRM||', Number of failures in EXCEPTION: '||n_failures);
END;
/

--#7
BEGIN
dbms_output.put_line('Materialized view data after first refresh');
dbms_output.put_line('==========================================');
END;
/

SELECT *
FROM mv_table1;
--#8
BEGIN
dbms_output.put_line('AFTER adding a duplicate record, the refrsh will raise error and refresh won''t happen successfully');
END;
/

INSERT INTO T_SALARY values(1,11000);

--#9
DECLARE
n_failures number:=0;
BEGIN
dbms_output.put_line('Materialized view second refresh');
dbms_output.put_line('============== 222 =============');
dbms_mview.refresh_dependent(number_of_failures => n_failures,
list => 'MV_TABLE1'
,atomic_refresh => TRUE
,nested => TRUE
);
dbms_output.put_line('Number of failures: '||n_failures);
EXCEPTION
WHEN
OTHERS THEN
dbms_output.put_line('Error: '||SQLERRM||', Number of failures in EXCEPTION: '||n_failures);
END;
/

--#10
/*
Output expected but NO value for number_of_failures (n_failures) in dbms_output line
PL/SQL procedure successfully completed.

Error: ORA-12008: error in materialized view or zonemap refresh path
ORA-01502: index 'PK_MV_TABLE1' or partition of such index is in unusable state, Number of failures in EXCEPTION:
*/

refresh_after_errors  => true,
atomic_refresh => false

nested => true,
out_of_place => true, 

delete t_salary;
insert into t_salary values ( 1,11000 );
insert into t_salary values ( 1,11000 );
commit;

declare
  n_failures number := 0;
begin
  dbms_output.put_line ('Materialized view first refresh');
  dbms_output.put_line ('============== 111 =============');
  dbms_mview.refresh_dependent (
     number_of_failures => n_failures,
     list => 'MV_TABLE1',
     atomic_refresh => false,
     refresh_after_errors => true
  );

  dbms_output.put_line ('Number of failures: ' || n_failures);
exception
  when others then
    dbms_output.put_line ('Error: '
                          || sqlerrm
                          || ', Number of failures in EXCEPTION: '
                          || n_failures);
end;
/
Materialized view first refresh
============== 111 =============
Number of failures: 0

delete t_salary;
insert into t_salary values ( 1,11000 );
insert into t_salary values ( 1,11000 );
commit;

declare
  n_failures number := 0;
begin
  dbms_output.put_line ('Materialized view second refresh');
  dbms_output.put_line ('============== 222 =============');
  dbms_mview.refresh_dependent (
     number_of_failures => n_failures,
     list => 'MV_TABLE1',
     atomic_refresh => false,
     nested => true,
     out_of_place => true, 
     refresh_after_errors => true
  );

  dbms_output.put_line ('Number of failures: ' || n_failures);
exception
  when others then
    dbms_output.put_line ('Error: '
                          || sqlerrm
                          || ', Number of failures in EXCEPTION: '
                          || n_failures);
end;
/
Materialized view second refresh
============== 222 =============
Number of failures: 1

Thank you Chris!
I can't choose the "number_of_failures" counter over the actual error. It is best to get both. I raised SR with Oracle.

Thank you for the comments and alternative options