Of, and the difficulty of explaining what it is.

I get annoyed when people write "could of". Aggravatingly, though, I'm not too good at explaining why.
I can tell them that what they are trying to say is "could have" and the problem comes from the fact that it is almost exclusively pronounced "could've" these days. The next question is inevitable: what's wrong with "could of"?

The explanation is extremely simple. "Of" isn't a verb, and if you remove the "could" before it, that becomes obvious:

"I could have gone swimming" becomes "I have gone swimming"
"I could of gone swimming" becomes "I of gone swimming".

This is difficult to explain, however, because the chances are if you're someone who doesn't know the difference between "could've" and "could of", you probably don't know what a verb is, either. Not due to stupidity or anything, just because the rules of grammar are not interesting to you... or perhaps because of stupidity.

Second language users of English don't have this problem, this is because they have to reconstruct what they want to say, they've had to learn the rules of English. For first language users this is a natural process. For example learning other tenses in different langauges seems very difficult for us, but in English we just naturally understand.