1) Applicable reliabilities: notably, internal consistency and stability over time (plus inter-scorer reliability in measures involving subjective judgment, e.g., projective tests or awareness-of-deception measures.
2) Applicable validity measures: notably criterion validity (e.g. , a short intelligence test 's correlation with the WAIS), convergent validity, discriminant validity and factorial validity.
Inter-rater reliability is only required where it applies, namely when a measure includes some element of subjective judgment, e.g. ratings of job candidates, scoring of projective measures, or awareness-of-deception measures. (Scoring TAT stories for achievement motivation is one example of a projective test.) Inter-rater reliability clearly does not apply to "objective" measures like Likert scales, Thurstone scales, multiple-choice tests, or true-false tests.