Spelling poorly is probably the fastest way for anyone to lose credibility.
(Spell-check programs are NOT reliable.)
Unless you are dyslexic, focus on excelling at spelling.
(If you are dyslexic, relax and thank your lucky stars that you have an excuse! You might also want to let your professors, supervisors, etc., know, though the spelling errors caused by dyslexia are pretty distinctive anyway, and don't have the same stigma attached to them. Incidentally, I know several brilliant academics who are dyslexic.)
A few words to memorize:
Argue but Argument
Explain but Explanation
Existence but Assistance
Believe but Conceive
Accept versus Except
Weather versus whether
The effects of something versus To affect something
Some words sound identical but are spelled differently.
E.g. Their versus There ("They will bring their best wine to the picnic there in the mountains.")
E.g. Your versus the contraction You're ("Your place or mine?" "Gosh, you're in a good mood, today!")
Distinguish between contractions, plurals, and possessives.
. Plural: Societies ("Most societies advocate treating children very well.")
. Possessive singular: Society's ("The U.S. society's wealth is distributed very unevenly.")
. Possessive plural: Societies' ("All societies' laws forbid incest."
. Contraction of singular "Society is": Society's ("Y'know, human society's more pleasant than solitude.") (Identical to the possessive singular; we have to determine which it is by its context.)
As with punctuation, you'll be surprised how quickly these will become second nature. You'll probably find yourself correcting the misspellings in dirty limericks on bathroom walls. The authors may even thank you.