How to use SELECT DISTINCT with RANDOM() function in PostgreSQL?

You can simplify your query to avoid the problem a priori:

SELECT p.cod, p.title
FROM   product p
WHERE  p.visible
AND    EXISTS (
    SELECT 1
    FROM   product_filter pf
    JOIN   filters f ON f.cod = pf.cod_filter
    WHERE  pf.cod_product = p.cod
    )
ORDER  BY random()
LIMIT  4;

Major points:

• You have only columns from table product in the result, other tables are only checked for existence of a matching row. For a case like this the EXISTS semi-join is likely the fastest and simplest solution. Using it does not multiply rows from the base table product, so you don't need to remove them again with DISTINCT.

• LIMIT has to come last, after ORDER BY.

• I simplified WHERE p.visible = 't' to p.visible, because this should be a boolean column.

You either do a subquery

SELECT * FROM (
    SELECT DISTINCT p.cod, p.title ... JOIN... WHERE
    ) ORDER BY RANDOM() LIMIT 4;

or you try GROUPing for those same fields:

SELECT p.cod, p.title, MIN(RANDOM()) AS o FROM ... JOIN ...
    WHERE ... GROUP BY p.cod, p.title ORDER BY o LIMIT 4;

Which of the two expressions will evaluate faster depends on table structure and indexing; with proper indexing on cod and title, the subquery version will run faster (cod and title will be taken from index cardinality information, and cod is the only key needed for the JOIN, so if you index by title, cod and visible (used in the WHERE), it is likely that the physical table will not even be accessed at all.

I am not so sure whether this would happen with the second expression too.

Use a subquery. Don't forget the table alias, t. LIMIT comes after ORDER BY.

    SELECT *
    FROM (SELECT DISTINCT a, b, c
          FROM datatable WHERE a = 'hello'
         ) t
    ORDER BY random()
    LIMIT 10;