I often look at what I write and wince. I'm never satisfied. There's always something to improve, a sentence to tighten, unnecessary clutter to remove. I write to be understood, unlike some literary works where the goal is to be misunderstood. Think of Joyce.
Although I try to write following Zinsser's advice (as stated in On Writing Well), I didn't learn it from Zinsser. What I know of it, oddly enough, can be traced to N. David Mermin's article in Physics Today called "What's Wrong With these Equations?".
When I started studying physics, my solutions work was bad. My old study method was to solve problems without explanatory prose, write equations and then obtain the solution. For simple problems, this was alright, but when I started solving more complicated problems, it was a major hassle. I suppose many mature physicists and mathematicians had to learn that one really does need explanatory prose because without it, say, 30 equations away, you would be lost.
It was a good thing that I spent some of my free time reading Physics Today, and it was doubly lucky that I read Mermin's article. If I recall right, I first read it while working on the third part of the mathematical methods in physics course (we have four semesters of it, and used Arfken's text for the first three semesters). Writing, I discovered, was a way to force myself to think clearly about physics and mathematics. If you followed Mermin's rules, you could use them to avoid deceiving yourself that you actually understand the material.
I was so impressed with Mermin's article so that when I first started tutoring math methods, I gave copies of Mermin's article to my supervisees, and had them apply it to their own solutions work. Since most of my thesis adviser's subgroup worked with me, you will find more than a few traces of Mermin's influence in how they write.
Zinsser's role was to codify many of the things I knew: Eliminate clutter; Keep it simple; Writing should please your inner ear. His book is always on my rereading list to remind myself that there is always something I can do better. One inspirational example is on page 10 of On Writing Well: what one of his drafts looks like. I can't do the same thing on a word processor; saving many versions does not show the editing process as well as writing by hand on a printed draft.
Knowing, sadly, doesn't necessarily mean doing well. Hence the need to edit, and the tendency to wince at what I wrote. That's also one reason I try not to reread my old blog posts-- since I'm never happy with what I write, I'd end up re-editing, which is not good use of my time. I can spend a lot of time composing and editing a new blog post, and the editorial work is hidden. I have to stop somewhere-- here, for example.