An interesting read. But I think the author should have explicitly written out the point he is really making: you can't be too careful about making your writing clear, even to yourself. I recall reading (I'd point to the book with a link if I could remember in what book I read this) that mathematicians who occasionally write expository articles on mathematics for the general public are often told by their professional colleagues, fellow research mathematicians, "Hey, I really liked your article [name of popular article] and I got a lot out of reading it." The book claimed that if mathematicians made a conscious effort to write understandably to members of the general public, their mathematics research would have more influence on other research mathematicians. That sounds like an important experiment to try for an early-career mathematician.
More generally, in the very excellent book The Sense of Style: The Thinking Person's Guide to Writing in the 21st Century,[1] author and researcher Steven Pinker makes the point that the hardest thing for any writer to do is to avoid the "curse of knowledge," assuming that readers know what you know as they read your writing. It's HARD to write about something you know well without skipping lots of steps in reasoning and details of the topic that are unknown to most of your readers. This is one of the best reasons for any writer to submit manuscripts to an editor (or a set of friends, as Paul Graham does) before publishing.
And, yes, if you think what I wrote above is unclear, as I fear it is, please let me know what's confusing about what I wrote. I'd be glad to hear your suggestions of how to make my main point more clear. I'm trying to say that anyone who writes anything has to put extra effort into making his point clear.
[1] http://www.amazon.com/gp/product/B00INIYG74/