Daniel Goepfrich wrote a substantial interaction with this blog over on his site – here – this post is specifically addressing the examples of poetry and prophets given in paragraphs 10 & 11.
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Regarding Poetry, again I don’t insist that we preach through a book – that is not what I teach (thanks for correcting your post on that). However, it would be a shame to miss the importance of written context for any biblical passage. Proverbs seems to be the most randomly organized, until you read Bruce Waltke or someone like that and start to see the structuring of apparently random collections of proverbs. Whether or not that can or should be communicated in preaching is another issue. Ecclesiastes and Job are not random collections. Psalms, I would suggest, is not as random as our contemporary hymn books (ordered alphabetically). It contains collections, and increasingly scholars are recognizing structure and ordering throughout the collection. My Hebrew prof did his OT PhD on the evidence of structure and order in Psalms 107-118. His mentor, Gerald Wilson, has demonstrated that Psalms is anything but a mere hymn book. Again, it would be a shame to have a superficial view of this part of the canon and miss some of the richness contained in the structure and sequencing of the book. That does not require preaching straight through, but it does urge us to have a real awareness of the literary context in our studies.
You mention prophets, and likewise, I agree that we don’t have to preach straight through. Again, though, I suggest that even if two oracles were given at different times, or in a different order, the way they are in the Bible now is the inspired text. Our task is neither to dismiss ordering of texts and treat them as random collections, nor is it to “reconstruct” an original and better order. Our task, in part, is to understand the inspired text as it stands. Whether you preach straight through or not is up to you – I do both. However, I would suggest that not studying a passage in context will seriously undermine your ability to understand the text (and why should you study in context if it’s just random?)
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My final segment of response will come tomorrow. Thanks.
Biblical Preaching 
Peter,
You said: “However, I would suggest that not studying a passage in context will seriously undermine your ability to understand the text (and why should you study in context if it’s just random?)”
I think this is really what it comes down to. I believe that whatever we are preaching/teaching, from whatever text (even if it’s just a few words of a passage) MUST acknowledge and be accurate to the original intent and context.
Regardless of the texts we choose or the order we teach them, we place ourselves under God’s judgment when we take them out of context and make them say what they never said.
Daniel