Dodawanie wyników instrukcji CASE

Brakuje END na Twoim CASE oświadczenia:

SELECT
  surname,
  givenname,
  (CASE WHEN surname = 'Smith' THEN 2 ELSE 0 END)  -- < add END
    + (CASE WHEN givenname = 'John' THEN 1 ELSE 0 END)  -- < add END
    AS score
FROM person
WHERE (surname = 'Smith' AND givenname LIKE 'J%')
  OR  (surname LIKE 'S%' AND givenname = 'John')
  OR  (surname = 'John' AND givenname LIKE 'S%')
  OR  (surname LIKE 'J%' AND givenname = 'Smith')
ORDER BY
  score DESC,
  surname ASC,
  givenname ASC;