Grammar Brigade: homonyms explained

What's a homonym?

Homonyms are two words which sound the same, but are spelled differently.

Let's look a few commonly misused homonyms:
It's vs. its; there vs. they're vs. their; let's vs. lets; you're vs. your; whose vs. who's; capital vs. capitol; principle vs. principal; passed vs. past

It's: A contraction of "it is."  Do not use anywhere you would not use "It is."
ex: It's purple.
Its: The possessive of "it."  Use when "it" owns something.
ex: Its hat is purple.

There: A place.  Should only be used when pointing at something, or in text when "there" has been clearly specified.
ex: It is over there. 
There: A way of starting a sentence in passive voice.  (Why are you using passive voice in your writing?  You'd better have a good reason.  No, really.)
ex: There is nothing worse than getting squashed by a falling toilet. 
They're:  A contraction of "They are." Use only when you would use "they are."
ex: They're in Georgia.
Their: The possessive form of "they." Use when they own something.
ex: Their car broke down in Georgia.

Let's: A contraction of "let us."  Use only as a substitute for "let us."
ex:  Let's go to Canada.
Lets: The present tense conjugation of "let" (as a synonym for "allow") for a singular person.
ex:  He lets me borrow his flour.

You're: A contraction of "you are."  Use only as substitute for "you are."
ex:  You're angry, aren't you?
Your:  The possessive of "you."  Use when you own something.
ex:  Your book bag is heavy.

Whose:  The possessive of "who."  Use when you are trying to determine the owner of something, or when you are using "who" as a pronoun.
ex:  Whose book bag is that?
ex:  I gave it to Jacob, whose book bag needed the extra space.
Who's:  The contraction of "who is."  Use only to replace "who is."
ex:  Who's responsible for the laundry this week?

Capital: A city that serves as the seat of government for an area, or an asset such as wealth, or a capital letter.
ex:  Raleigh is the capital of North Carolina.
Capitol: Only used to name a building; specifically, the building in which the legislature meets.
ex:  We were really bored during our tour of the Capitol Building.

Principle:  A moral purpose.
ex:  It's against my principles to eat raw steak.
Principal:  An adjective meaning most important, or the leader of a school, or the initial investment of money before interest is added.
ex:  The principal objective is to not get eaten by the dinosaurs; after that, you need to capture the flag.

Passed:  The past tense of the verb "to pass."  Use only if someone has physically moved from behind to ahead of something, or passed a test.
ex:  I passed the test with flying colors.
ex:  He passed me in the right-hand lane.
Past: A location; a time period; a preposition; an adverb; "past" locates something in time and space.
ex: I stuck my tongue out as I drove past him.
ex: One look at the funny breeches told him everything: he was stuck in the past, with no way home.
ex: In my past life, I was an osterich.
ex: The days for mourning are now past.
ex: It was half past three.
What are the most common homonym mistakes you see?