Quite simply Smith was NEVER overwritten
Think about what happened with the Oracle. The Mero had her SHELL terminated, but her program process opened a new shell. Here is exacly what is said between Neo and the Oracle in Revolations:
Oracle: Do you recognize me?
Neo: A part of you.
Oracle: Yeah, that's how it works. Some bits you loose some bits you keep. I don't yet recognize my face in the mirror, but....I still love candy.
Neo: No, thank you.
Oracle: Remember what you were like when you first walked through my door, jittery as a june bug? And now just look at you. You sure did surprise me Neo and you still do.
Neo: You gave me a few surprises too."
Smith: Every mammal on this planet instinctively develops a natural equilibrium with the surrounding environment. But you humans do not. You move to an area and you multiply and multiply until every natural resource is consumed and the only way you can survive is to spread to another area. There is another organism on this planet that follows the same pattern. Do you know what it is? A virus.
Smith became a virus, but everyone got stuck on Smith's own words when he said "I don't fully understand how it happened. Perhaps some part of you imprinted onto me, something overwritten or copied." Because everyone keeps talking about Smith being Overwritten. If he was overwritten, there would have to be a full, new Smith to copy over the old one. This is, ofcourse, not the case since Neo did not program a smith agent. My point is that the same thing that happened to agent Smith is the same theory behind someone breaking the copy-protection on a computer program to use it for free. There is a set of programming code made up of bits that must be deleted or altered in order to render the program usable without paying for the code that is needed to use it.
Originally posted by shaber
A hole! What happened to the knotty point of the sky being torched? How can the machines afford to free the cyborgs? And then it never explained whether there was a civilisation of machines or whether they are all controlled by one consciousness...
as Mordecai says -
watch the Animatrix there are two short films on it that will give the history lesson you require to fill in the holes in your knowledge