“Dear Polish friends: I’m doubly sorry”, Knuth wrote at the top of a macro! “I’m doubly sorry that I have only a crude approximation to an ogonek”; and he went and drafted a macro to make an ogonek.
Now that was not a symbol that either appeared frequently or formed part of the mathematics of the paper. It was only required in the last two references, out of a total of 29. He used it on the last one but missed it on the other! As a sideline he used a comma to imitate the cedilla hook.
If you are interested, the paper is titled Overlapping Pfaffians. Knuth also took care of the spacing in the “Pfaffians” and for which he defined a macro as:
Moral of the story: Even the best of us can miss something, so always have someone else read through your final copy.
One can never be sure how much editing he did, but this particular paper showed seven revisions, with the dates all carefully marked at the top of the TeX file and spanning some three months. If you follow some of the guidelines in this answer and analyze Knuth’s publicly available works, you can observe that:
Overfull boxes are down to none on all his papers. He used very few additional fonts. At most he defined a short-cut for the small caps font, normally as
\font\sc=cmcsc10. Knuth is very consistent with spacing. Most displayed equations are treated as paragraphs and they are compactly inserted between the text. They also have the correct punctuation after the equations.
There are no rivers, almost no bullet lists and where lists exist, they have a function; mostly to describe steps in algorithms. Talking of steps, have a look at the step diagram below, from another Knuth paper, where he used it to indicate the number of ways to put a positive integer into a k-rowed triple staircase:
It took this to write it, I am sure, just so that the line thickness would match with the text:
He took care of hyphenation, where there was a problem, both preventing it as well as encouraging it where it was appropriate.
What is prevalent in his works is consistency, which I think is one of the most valuable traits of good typography
Now to summarize the response to your questions:
Did the original author of TeX make such small adjustments to specific words within his books? Yes, as is evident from the above.
How critical is the order in which one completes these tasks? E.g.: if I modify something at the end of my document, then modify something at the beginning, is my first modification now irrelevant? Are there times when it is better to fix a problem near the end of a document first? If order is important, in what order is most efficient?
Dijkstra — the famous Computer Scientist — allegedly wrote his famous EWD notes in one pass and never went back to revise them. This is obviously the most efficient method of editing a document; if you are a genius. For us mere mortals we can do well to follow Halmos editing algorithm. When you finish Chapter 2, go back and edit Chapter 1 and Chapter 2. When you finish Chapter 3, go back and edit Chapters 1–3 and so on. By the end of the Book, you only need one more edit from Chapter 1 to the last one and you are done. This is a good method for editing paragraphs in a Chapter as well. In my opinion this spiral technique is the most efficient — after Dijkstra's. True for the writing and true for the coding and true for many other things in life as well.
What are ideal ways to solve each kind of problem when they are encountered? There are no ideal ways as there are no ideal books, just information and advice, which you need to absorb and develop your own techniques.
Are there any books or articles which provide such information (e.g. a checklist outlining the above)? There is no checklist as far as I know floating around but Barbara’s answer to your question has one good point; read the guidelines. There are too many books on typography, most of them hijacked by Graphic Designers with plenty pictures of posters with fonts. Stir away from them. Best learn by example; study good papers and books in your field and try and emulate them; develop good habits. There is also good advice — most of the time — on this Site.
Style references: APA, MLA, Chicago Manual of Style,Oxford.
Similar but free guide aaanet. Excellent but a bit dated book on uses
of italics, which is a common source of inconsistencies and errors. The EU Style Guide, has a good section on romanization, another common area of inconsistencies. Best guide IMHO is the Economist's, unfortunately not free, but advice from people that write daily and make a living out of it is invaluable. The Magazine itself is reputed to have graphics that adhere to Tufte's guidelines. For maths see mathematical typesetting
Consistency: fonts, margins, headings, citations, bibliographies, contents, indices, list of symbols, page numbering, headers and footers are all well covered by (La)TeX, search for any problems tex.sx . Once you settle on a class, the best you can do is develop some macros of your own, e.g., names you are prone to get wrong while typing for example names such as Hàn Thế Thành, abbreviations etc.
Inspiration: The physics website arXiv can be a source of inspiration, even if not your field. Quite a few of the papers provide the LaTeX or TeX code; but you can also get disappointed to read papers with almost 600 co-authors, where you could expect that there was at least a one typographically inclined co-author and find that the plots could do with a bit of TiKZ or pstricks magic and with a Jake answer. Best inspiration is to visit a good library, get a few books you like and study the style.