How vocabulary tests are graded depends on the teacher's (implicit or explicit) language learning or teaching theory. There are many such theories (see e.g. What are the main foreign language teaching methods?) with different views on how vocabulary should be taught (and tested).
In addition, there can be individual differences between teachers that subscribe to the same language learning or teaching theory. (Even in the context of standardised language tests, evaluators should regularly attend seminars in order to make sure that they all use the same evaluation criteria. See Bausch, Christ & Krumm (eds.): Handbuch Fremdsprachenunterricht, 5th ed. A. Francke, 2007, page 376.)
Language teaching theories that prefer a direct method teach vocabulary in context, while theories that allow the use of L1 let learners study associated pairs (L2 word - L1 translation). These approaches also determine how vocabulary is tested, e.g. through translations or by other means (cloze tests, building sentences with a given word, ...).
In both cases, the evaluator or teacher needs to weight the errors. For example, Englische Fachdidaktik. Theorien, Praxis, Forschendes Lernen by Wolfgang Gehring (Erich Schimdt Verlag, 1999/2010) lists the following types of minor versus major errors:
- Errors against general language rules.
- Errors that seriously hamper understandability.
- Errors against the current language learning goal (i.e. something that was taught very recently).
- Errors against "common construction".
- Strong deviations from language rules and stylistic norms.
- Errors against specific language rules.
- Errors that do not seriously hamper understandability.
- Minor deviations from "common construction".
- Minor deviations from language rules and stylistic norms.
The above error types apply to language tests generally (i.e. essay composition, oral skills tests, ...) and do not apply well to vocabulary that require translations (L1 to L2, or L2 to L1). In the current communicative approaches, simple word translation tests are often replaced by other types of tests, e.g. given a specific word, build a sentence that shows that you know the word's meaning. Errors in such sentences would need to be weighted according to the criteria listed above.
However, there are also vocabulary learning techniques where the only criterion is correctness. One example is SAFMEDS (Say All Fast Minute Each Day Shuffle). SAFMEDS is a technique that is part of precision teaching, a method of teaching and evaluating developed by Ogden Lindsley in the 1960s (and inspired by behaviourism). In SAFMEDS, you get through a deck of flashcards using the following method:
- You say the word on the other side of the card.
- You try to get through the deck within a minute.
- You put aside the flashcards where you made errors. (The number of errors is tracked in a "celeration chart".)
- You shuffle the deck after each run through the deck, so you don't memorise the sequence of cards.
- You do this every day.
(To get an idea of what SAFMEDS is, see e.g. SAFMEDS Tutorial by Kelly Byrne on YouTube, Vocabulary Aquisition with SAFMEDS: How to learn words quickly by Dr. C. A. Young-Pelton, and Surviving on SAFMEDS by Danielle Costa.)
Another teaching method where frequent formative tests play an important role is mastery learning, an instruction approach first formulated by Benjamin Bloom in the late 1960s. In mastery learning, all learners need to achieve a specific level of mastery before moving on to the next "lesson". Mastery learning has also been used in language teaching. However, I have not yet found literature that discusses grading of errors. For example, "Mastery Learning in Modern Languages - a Case Study" (Parkinson, B. L.; Mitchell, R. F.; Johnstone, R. M., 1983) discusses the use of mastery learning for teaching French in two schools in Scotland. The article does not mention the weighting of errors.
So "how correct is necessary" is highly dependent on the learning theory. There are vocabulary learning methods that are more effective than others, but some of the existing methods have probably not been compared yet (e.g. SAFMEDS versus the SuperMemo algorithm).