When Morpheus traps one of the Twin's arm in a door and shoots it, why doesn't the Twin Ghost and pass through the door? Instead the other Twin has to threaten Trinity so Morpheus will open the door.

Because as he ghosts, the door would shut, thereby preventing him from passing. Which brings up the thought if he's already part way through the door, would the act of the door closing while he's half-way through, kill him? (As the destination of the door would change.)

If Smith is no longer working for the system and appears to be working as a free agent, why does he help the Matrix octopus bots take out the ships from Xion? For that matter, why do the bots leave him alive (he's the only one, apparently)?

Good question. I assume we'll have an answer in the next movie. But it is given that the Matrix is trying to shut him down, if you look at the dialogue before the fight scene with Neo and the 100+ Virus Smiths.

They never did really explain where Smith suddenly got the ability to act virus-like, either...

Sure they did. When Agent Smith fought Neo in the first movie, some of the Neo's code ended up transferring into (now) Virus Smith due to a system glitch.

Aha! to that last answer. :)

basically... about Agent Smith...

there are more than just 2 levels to the matrix... which, wasn't actually explaned in the movie... but it will be in the 3rd I'm guessing.

I hope they don't use that trick. But yes, it is a definate possibility given how they set things up...

I'm kinda expecting something like "The 13th Floor" ...if they do that then... COP-OUT. um, though I can think of a few other optional routes they could go.