GENERAL WRITING RUBRIC
How to organize thoughts, focus thoughts, create an impression (audience awareness is part of that--and audience awareness is at once a mystery and simpler than you think), flow (how to pace, what details to include and leave out), how to persuade through reason, emotion, and authority; how to use sources appropriately; ability to create a focused argument and support it.
Critical and creative thinking
Reasoning ability, ability to look at the parts of an issue and draw reasonable inferences; the ability to analyze one's sources and look at their parts and draw reasonable inferences about these; an avoidance of simple logical fallacies such as hasty generalization (overgeneralization); awareness of one's own biases and accountability for them; an ability to look "outside the box" and consider new or unusual perspectives, different from conventional wisdom or one's own sources; ability to create a focused argument and support it in a reasonable and insightful manner.
Ability to write appropriately for the task at hand. Appropriately does not mean slavish adherence to conventionality, but a sense of the purpose of the writing and ability to guide it toward fulfilling that purpose, with awareness of the audience's potential reactions and needs. As you grow in academic writing experience, you'll encounter more types of academic genres: researched arguments, reports, reviews, summaries, personal testimonies, letters of admission to programs or clubs, journalistic documents, different kinds of analytical essays or reports. The best guide for genre at this point is the assignment that I provide. Part of this knowledge is knowing how to choose appropriate sources for information and cite them correctly in your papers.
This is an odd way of lumping together "the rest" of the stuff that makes writing polished and effective, such as following conventions of grammar and punctuation and formatting one's papers correctly and/or effectively (if the format is one's choice, choosing the appropriate format for the paper). Effective proofreading.