The stories of the two men who were contemplating adultery is a working summary of the distinction between what one's deepest desires will lead to in behavior. Leveraging so much from ideas by Thomas Brookes and John Owen may just mean that this segment was going to be alright.
It still seems a bit odd to describe the world as "corporate flesh" and then not really get too much into the flesh beyond generalities. Do we say the flesh is the propensity of fleshly weakness to be susceptible to sin? Well, perhaps not because the body is not necessarily an evil. We could try to digress into natural vs federal imputation a la John Murray's The Imputation of Adam's Sin but why bore literally everyone who hasn't gotten at least three books from monergism.org?
But there's something worth noting since there are some folks on the internet who have claimed new Calvinists go so far as to say Christians aren't regenerate and retain a sin nature. Driscoll explicitly repudiated that idea in 2008:
I don't think a believer has a sin nature. I believe we have a new heart by the power of the Holy Spirit so I wouldn't say that a Christian's essential nature is total depravity and nothing but sin but I would say there are conflicting desires within a Christian between their regenerated nature and the Holy Spirit and their new heart and their flesh which is still that, that seed of rebellion from Adam in them that wants to disobey.
So where Driscoll's concerned, it's not possible to say Driscoll thinks Christians have a sin nature. He may have a sloppy understanding of the nature of sin itself and of the flesh and its desires ... but it can't be said he somehow imagines Christians have sin natures as such.
Driscoll wrapped up part 1 with a few observations that many evangelicals could find basically agreeable. It's worth reminding readers that this larger and broadly orthodox (if simplistic) notion of spiritual warfare is the frame in which a couple of specific statements were made. The most important of these statements was condemning a "myth" that the executive elders of Mars Hill didn't love the church as "a demonic lie". If cessationists were to consider the session not as a doctrinal tract, as such, but as also being a political act/statement within Mars Hill, we may get some insight into how Mark Driscoll dealt with the leadership culture.
If Part 1 had a few strange moments here and there (such as a number of implausible stories framing some recyclings from Puritans) Part 2 of Spiritual Warfare was where Driscoll cut loose. That's where Driscoll began to sound off on women as gossips and bitterness as a demonic foothold and got into the "ordinary demonic" and opening straight out the gate with insufficient sex.
But transcribing that magic will take some time.