The most common mistake
I am sure it must be true: the most common mistake in English writing is to use "it's" as a possessive. I know we are all taught this in primary school. "It's" means "it is". Nevertheless, it is a common comment from examiners to PhD candidates:
"You have made the most common mistake in English writing here. "It's" is a contraction of "it is" and that is the only time an apostrophe is used. "It's a beautiful day" is correct, whereas "The car lost it's control on the slippery pavement" is incorrect. The way to tell whether to use "it's" or not is to substitute "it is" and see if it makes sense. Remove the apostrophe here and wherever else it may be used incorrectly."
Now I know we all know this; nevertheless, this is one of the most common comments made by examiners. Perhaps the linguists among us will tell us whether this confusion actually is the most common mistake in written English. When I checked the web I found a wide variety of claims as to what is the "most common mistake in written English": Your vs. You're; It's vs. Its; There vs. Their; Affect vs. Effect; and the Dangling Participle were high on the list. Also popular were missing articles and spelling mistakes.
The usual convention in scholarly writing is to avoid all use of contractions. The use of contractions creates a familiar tone and does not sound as serious as spelling out the words in full.