I tend to make the same set of comments over and over when I proofread scientific writing, so I thought I'd gather them together into one place for easy reference.
  1. Comma usage.
    1. Use a comma after "but", "next", "here", "now", "then", adverbs etc., when starting a sentence. Then, your text will flow nicely.
    2. If your sentence has one, always use a comma to set off a leading prepositional phrase.
    3. Use commas to set off "parenthetical" type phrases, common in many people's writing, embedded in the sentence.
    4. As you, I, and everyone else knows, commas are important in lists.
    5. It is customary to use commas when joining two sentences together into one, so don't forget.
    6. Use "which" only after a comma, because it is used to add descriptive features instead of defining features. So, "the ball which I threw" should either be "the ball that I threw" (meaning, "of the many possible balls, I'm talking about the thrown one") or "the ball, which I threw" (meaning, "that ball I'm talking about, you might also like to know that I threw it"). Of all the rules that I have learned, I make a special effort to follow this one, which I learned from my advisor.
    7. Avoid using commas for situations not on this list even if you want to add one because it feels like you want to take a breath.
  2. Apostrophe usage.
    1. Pluralize abbreviations using an "s". So, use "MDPs", not "MDP's" to mean "Markov decision processes".
    2. Master "its" vs. "it's". "Its" is possessive and "it's" is a contraction for "it is". So, we say "It's unfortunate that its nose fell off." In my experience with this rule, it's common for people to forget its proper usage.
  3. Clear, direct language.
    1. Avoid the dangling "this". So, "this example shows that" not "this shows that". This rule is intended to discourage this kind of behavior. One hint: Try changing "this" to "it"---usually, doing so will make it obvious that more context is needed.
    2. To avoid cluttering your sentences, change "in order to" to simply "to".
    3. To use simple words when appropriate, change "utilize" to "use".
  4. Dash/hyphen usage.
    1. Hyphenate noun phrases if they defy the natural right-to-left grouping in English. So, "algorithm for reinforcement learning" is ok, but "reinforcement learning algorithm" should be "reinforcement-learning algorithm". Noun-phrase hyphenation is needed to group words in the beginning of a noun phrase, but not when there are only two words. [A nice example from The Colbert Report: "Nazi-treasure hunter" (someone seeking Nazi treasure) vs. "Nazi treasure hunter" (a Nazi who is seeking treasure).]
    2. Know when to use different lengths of dashes. It is state-of-the-art usage to employ a short dash (hyphen, single dash in LaTeX) within words. Ranges require a slightly longer dash; they are written with a double dash (en-dash) in LaTeX as explained in pages 14--33 of Lamport's LaTeX guide. To set off a phrase---something many people do---use even longer dashes with no spaces before or after them (em-dash, written as a triple dash in LaTeX).
  5. Usage related to confusable pairs.
    1. led/lead. Perhaps because of the pronunciation of the name of the element "lead", some people are led to believe that the past tense of the verb "lead" can spelled the same way.
    2. affect/effect. They are pronounced similarly and they both can be used as nouns and verbs. It's a recipe for disaster. It affects the clarity of your writing if you mix up these words. The end effect is that people are frustrated because they aren't sure what you said. You can effect change in their affect if you get it right the first time.
    3. bare/bear. Bear with me, because you'll want to bring the right rule to bear. "Bear" can mean the animal or various things related to the idea of exertion. "Bare" is connected with nakedness. They seem quite unrelated but sometimes people can barely tell the difference. I guess you just need to grin and bear it with your bared teeth.
    4. it's/its. See 2b. (Or not 2b.)
    5. dissertation/thesis. The "dissertation" is the document and the "thesis" is the claim made by the document that the document supports. Every dissertation should explicitly state its thesis.
    6. their/there. "There" is the answer to "here?" while "their" describes something an heir might own. Although it's taking me awhile, I'm starting to warm up to "their" as a singular, genderless modifier. There is a difference in spelling between these words and it's important to be able to distinguish their usage. (Suggested by Morgan McGuire.)
    7. hear/here. "Hear" is what you do with your ear and "here" is the answer to "There?" (See 5f.) Around here, we don't like to hear about people misusing these words. (Suggested by Morgan McGuire.)
    8. shear/sheer. When someone cuts your hair with a shear, make sure your ear is safe, and sheer pleasure is so pure as to make you go "ee!". If misusages were fleece, you'd want to shear them off for the sheer joy of being right. (Suggested by Morgan McGuire.)
    9. fair/fare. The verb "fare" means to go or travel, the noun "fair" is a festival, and the adjective "fair" denotes a lack of bias. Did you fare fairly well in your understanding of this example? (Suggested by Morgan McGuire.)
  6. one- vs. two-word phrases. These phrases should be one word when used as a noun and make up two words when used as a verb. Examples:
    We trade off time and energy to strike a careful tradeoff.
    We cut off any runs that went beyond the 10% cutoff.
    We print out the data and pick up the printout later from the pickup box.
    I will write up my experiment and then send the writeup to my supervisor.
    More: follow up, followup; speed up, speedup; set up, setup; in line, inline; make up, makeup.
  7. Paper structure.
    1. Don't use citations as nouns. Say "As explained by Kearns and Singh (2002)" or "As explained in the literature (Kearns and Singh 2002)" instead of "As explained by (Kearns and Singh, 2002)". This rule is summarized by Kaelbling and Cohn (2001), along with many others that I've included.
    2. Don't use latin abbreviations. That is, say "that is" instead of "ie" or "for example" instead of "eg". I guess I don't mind Latin if it's spelled out, for example "ad hoc". But, no one seems to use "exempli gratia" (e.g.) and "id est" (i.e.), for example, because they seem unnecessary, that is, there are perfectly good English substitutes.
    3. Avoid empty sections. Some text is needed between a section title and the first subsection of the section.
    4. Capitalize names of structural items like sections, equations, figures, and tables, as in "Section 3.1". So, "next section", but "Section 6". The same rule applies to "Item 2", "Table 3", "Assumption 4", and "Theorem 1.5".
    5. Don't begin a sentence with a variable or function name. It can help to put "The equation ..." in front of it first.
    6. Put punctuation after an equation, especially if it ends a sentence.
    7. Every paragraph, section, paper, chapter, and dissertation should have a topic sentence.
Updated by Michael L. Littman, 2012, 2014. All rights reserved.

(Littman style guide. Littman grammar rules. Littman comments. Littman usage. Littman style file. Littman seems to think he can get Google to search his own files better than he can.)