SQL REGEXP_SUBSTR retorna String nula ao dividir

Basta usar REPLACE e seu código padrão com ,

SqlFiddleDemo

 with temp as
(
    select 108 Name, 'test' Project, 'Err1:::Err2:::Err3' Error  from dual
    union all
    select 109, 'test2', 'Err1' from dual
)
select distinct
  t.name, t.project,
  trim(regexp_substr(REPLACE(t.error, ':::', ', '), '[^,]+', 1, levels.column_value))  as error
from 
  temp t,
  table(cast(multiset(select level from dual connect by  level <= length (regexp_replace(REPLACE(t.error, ':::', ', '), '[^,]+'))  + 1) as sys.OdciNumberList)) levels
order by name

Ou você precisa dividir pelo comprimento do delimitador:

SqlFiddle

with temp as
(
    select 108 Name, 'test' Project, 'Err1:::Err2:::Err3' Error  from dual
    union all
    select 109, 'test2', 'Err1:::Err2' from dual
)
select distinct
  t.name, t.project,
  trim(regexp_substr(t.error, '[^:::]+', 1, levels.column_value))  as error
from 
  temp t,
  table(cast(multiset(select level from dual connect by  level <= length (
       regexp_replace(t.error, '[^:::]+'))/3  + 1) as sys.OdciNumberList)) levels
order by name

Você pode ver por que executar:

SELECT length (regexp_replace('Err1:::Err2:::Err3', '[^:::]+')) + 1 AS l
FROM dual

Isso retornará 7 e seu:

SELECT DISTINCT  t.name, t.project,
trim(regexp_substr(t.error, '[^:::]+', 1, levels.column_value))  as error

tentará obter regexp_substr para 7 ocorrências onde 4 delas serão NULL e no final 4 NULL será reduzido a um NULL por DISTINCT .