PostgreSQL does error handling with the RAISE statement. Any errors will be caught in the RAISE statement when it's used. 

The following query will try to insert values into the allstarfull table and use RAISE to output the error:

DO $$ 
BEGIN 
INSERT INTO allstarfull 
(playerid, yearid, gamenum)
VALUES ('aaronha01', 1958, 0);

exception when others then 
RAISE notice '% %', SQLERRM, SQLSTATE;

END $$;

You will receive an error with those variables set as-is because there is a primary key violation: 

duplicate key value violates unique constraint "allstarfull$index_2bd68208_c8b4_4347" 23505

To learn more about error handling in PostgreSQL, take a look at the Further reading section.