Apostrophe - my pet peeve - usage

Hi. For whatever reason, I get really irked when I see mis-used apostrophes. I really don't know why, except that it's not because my grammar is all that superior (trust me on that one).

So I'm posting to ask a couple of apostrophe questions.

First, I notice that grammarbook.com's (great site, btw) http://www.grammarbook.com/punctuation/apostro.asp does not allow the use of apostrophe s ('s) to indicate is, like was done on this Barron's headline: Mobile Party's Just Starting.

Barron's does that often. I was bored today and wrote the editor a quick email, he replied that it is grammatical and accepted usage. Is that usage really OK?

Second, can you write , (from the same apostrophe page)

Please dot your i's.
You don't mean is.

Ted couldn't distinguish between his 6's and 0's.
You need to use the apostrophe to indicate the plural of zero or it will look like the word Os. To be consistent within a sentence, you would also use the apostrophe to indicate the plural of 6's.

like this, instead:

Please dot your 'i's.
Ted couldn't distinguish between his '6's and '0's.

or like this:

Please dot your "i"s.
Ted couldn't distinguish between his "6"s and "0"s.

Because I don't like the way those are written in the first example. It implies possessive, which is not right. Since I am a math major, I write a lot of solitary numbers and letters (e.g., let x represent...). I am starting my thesis, so I this is a big issue for me.

Thanks,
Jeff

P.S. How's my grammar in this email?