It depends on the objectives of the exam. Usually coherence and cohesion, punctuation, tenses, choice of vocabulary, words order and verb-subject agreement are among major issues to be assessed in writing exams. In other words, to check that it is grammatically accurate with a good coherence and cohesion.
I agree with Faisal Mustafa. You can use a rubric, but I would suggest adding other writing components, Coherence and cohesion, spelling, punctuation marks, paragraphing, clarity and completeness.
The key features are mentioned by my colleagues but in different order. I would order them as: grammar, punctuation, organization, content, coherence, and conciseness.
In addition to focusing on the linguistic issues at the morphosyntactic level such as grammar, spelling, punctuation, vocabulary and so on, writing exams need to be built with attention paid to issues at the discourse level such as cohesion and coherence.