"It's" and "who's" are very frequently "misused". I believe explanation of their "proper" use merits an article.

It's: "it is" (or "it has"). "It's" is non-possessive, and, as evidenced by the apostrophe, "it's" is a contraction.
Usage examples:

• "It's the last thing I ate."
• "It's been pretty rainy, as of late."

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Its: possessive form of "it".
Usage examples:

• "Its thick fur protects it from the cold."
• "Its claws are pretty strong."

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Who's: "who is" (or "who has"). "Who's" is non-possessive.
Usage examples:

• "Who's been eating my lunch?"
• "You're the one who's been doing that."

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Whose: the possessive form of "who".
Usage examples:

• "Whose shoes are those?"

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Generally, in serious writing, people do not mistake "who's" for "whose" and "it's" for "its". Though, I am aware that the relevant literary facts are ultimately constructed rather than discovered, and I concede there is in fact a notable demographic that does use "who's" as "whose" and/or "it's" as "its".

As long as you're consistent, it's perfectly acceptable to refuse to employ the distinctions presented in this article; however, I do consider it favorable to employ these distinctions, because they can facilitate quickly identifying the exact proposition(s) someone is trying to convey.