Syntax error when using exception inside for loop
As stated above in the comment, what I was missing was another BEGIN enclosing the exception.  

Updated code:

CREATE PROCEDURE run_all_scheduled_tasks()
LANGUAGE plpgsql
AS
$$
DECLARE
    rec record;
BEGIN
    FOR rec IN SELECT * FROM some_table LOOP
        BEGIN
        -- Statement 1..2..3..4
        EXCEPTION
            WHEN others THEN
                RAISE NOTICE 'Error Occured! Code: %, Messege:%', sqlstate, sqlerrm;
                ROLLBACK;
        END; 
        COMMIT;     
    END LOOP;

END;
$$;