The most common grammatical error on student papers has been the incorrect use of the possessive case. Pay attention to paragraph structure. Use topic sentences or transition sentences to begin each paragraph. Do not address new topics in the middle or at the end of a paragraph. Write in the active voice.
Bureaucrats often use the passive voice to avoid responsibility for bad decisions.
It is perfectly all right to go back over your paper with a pen to make corrections. Not doing so might be a big mistake. Every college student should have a copy of the small paperback book, The Elements of Style, by William Strunk and E. B. White. Spend five minutes looking through it before you begin writing. Spell-checking is a marvelous invention, but it is a poor substitute for proof reading.