the matrix - Is there anything special about Agent Smith that makes him become a virus?

If Neo had killed either of the other two agents instead of Agent Smith, would the killed agent have become the "Smith"-like virus as well?

Answer

I think there are at least some hints Smith was unusual before he became a virus. In the scene of Morpheus' interrogation, at one point Smith says "Leave me with him. Now." The other two agents give him an odd look before leaving, as if this is an unusual request. Then once they are out of the room, he removes both his sunglasses and his earpiece and says:

Can you hear me, Morpheus? I'm going to be honest with you. I hate this place, this zoo, this prison, this reality, whatever you want to call it. I can't stand it any longer. It's the smell, if there is such a thing. I feel saturated by it. I can taste your stink. And every time I do I feel I have somehow been infected by it. It's repulsive, isn't it? I must get out of here. I must get free and in this mind is the key, my key. Once Zion is destroyed there is no need for me to be here, don't you understand? I need the codes. I have to get inside Zion, and you have to tell me how. You're going to tell me or you're going to die.

So it seems he was highly motivated not just to do his job, but to find a way of destroying Zion so he could stop doing his job and leave the Matrix, which seems unusual for a program. And the fact that he ordered the other agents to leave and removed his earpiece (which seems to connect them to each other and to whatever other programs give them orders) before giving this speech suggests that he didn't want any of the other programs to know about these desires of his.

The removal of the earpiece is also important because at the start of Reloaded, he appears at the door of the rebel hideout and passes a package to the doorman, "Corrupt":

Smith: I'm looking for Neo.

Corrupt: Never heard of him.

Smith: I have something for him. A gift. You see, he set me free.

Then when Neo opens the package, he sees it's Smith's earpiece, which he no longer wears in Reloaded and Revolutions. So the fact that he associated the loss of his earpiece with being set free, combined with the fact that he removed it in the interrogation scene before he was transformed into a virus, suggests he already had an unusual desire to be free of his assigned role in the first film.

So while I don't know if another agent would have gained special powers from Neo destroying them in the same manner as Smith was destroyed in the first film, even if they did, I don't think another agent would have used these powers in an attempt to destroy the Matrix by copying themselves into everyone else inside it (a 'virus'-like strategy that may have been inspired by his notion that humanity was a kind of virus, something he talked about in another section of the interrogation scene with Morpheus).

As for the question of why Smith gained these new powers, I think all we really know is what was said in this exchange from Reloaded:

Smith: Then you're aware of it.

Neo: Of what?

Smith: Our connection. I don't fully understand how it happened. Perhaps some part of you imprinted onto me, something overwritten or copied. That is at this point irrelevant, what matters is that whatever happened, happened for a reason.

Neo: And what reason is that?

Smith: I killed you, Mister Anderson, I watched you die... With a certain satisfaction, I might add, and then something happened. Something that I knew was impossible, but it happened anyway. You destroyed me, Mister Anderson. Afterward, I knew the rules, I understood what I was supposed to do but I didn't. I couldn't. I was compelled to stay, compelled to disobey. And now here I stand because of you, Mister Anderson, because of you I'm no longer an agent of the system, because of you I've changed - I'm unplugged - a new man, so to speak, like you, apparently free.

The line "I don't fully understand how it happened. Perhaps some part of you imprinted onto me, something overwritten or copied" probably suggests the Wachowskis didn't really want to get into the specific technical details of why the transformation happened on a technical level.