If an idea originating in your brain successfully ends up, more or less intact, in my brain, then you have used language correctly -- regardless of such niceties as formality level, spelling, complexity of grammar, or number of emojis you use. If the idea ends up mangled or isn't transferred at all, then you have used language incorrectly. That is the only valid metric for correct and incorrect language use.
Language may be used suboptimally, in that e.g. failing to modulate your formality level to your audience can reduce your audience's opinion of you. (Which goes both ways -- the problem looms equally large whether you're speaking lolcat at an academic conference or using $10 words and academic jargon to trash-talk your Fortnite opponents.)
High-stakes standardized exams, colleges, and many employers all expect a certain level of mastery of formal Standard American English (SAE). I, as a teacher, am expected to prepare students for standardized tests and job and college applications. There is some tension here between this expectation and my personal beliefs.
Personally, my natural mode of communication is somewhat formal (even, some might say, highfalutin') SAE, occasionally meshed with the jargon of Internet memes, so I can naturally teach SAE by modelling it, and by assigning readings of SAE, and I can teach code-meshing by modelling it. Reprimanding students for 'improper' informal English serves more ill purposes than good ones, and vocabulary words and quizzes are well-established in the literature as being of limited value.
Not every assignment should require formal SAE writing -- it is effectively a foreign language for some students, who may more naturally speak, for example, African-American Vernacular English. To require mastery of SAE exclusively privileges some students (mostly white) over other students (mostly Black and English Language Learners), regardless of whether or not they have good or creative ideas, and regardless of what we're actually interested in assessing: whether or not they understand the content. Requiring mastery of SAE to the exclusion of all other Englishes is not just testing the fish against the squirrel on their tree-climbing abilities (as the quote commonly misattributed to Albert Einstein goes); it may be tantamount to requiring the student fish and squirrel to first walk to the tree they'll be tested on climbing.