I think this sentence would be better if we put an additional 'the' before the word 'students' So the sentence will become : it could be dangerous to carelessly teach grammar to the students
Judging from the structure of the sentence, there is nothing wrong with it. But if you analyze this sentence, there is just something minor that is missing. Perhaps, it would be better if we add the word "the" before the word "students". So the sentence would be, "It can be dangerous to carelessly teach grammar to the students." I hope this answer helps.
