There is an ISO standard relating to mathematics (although widely ignored?). The isomath package (http://tug.ctan.org/tex-archive/macros/latex/contrib/isomath) helps dramatically.

The differential operator should be roman, and care should be taken with spacing.
The constant ‘e’ should be in roman, as should all constants (excluding those whose values are experimentally determined, and therefore subject to change).

Please, someone, write a package to fix this. Csquotes is not the solution, because it adds a huge number of necessary keystrokes and hurts readability of the raw latex code and doesn’t solve the cut-and-paste problem. All that is needed is something that goes through the latex document and whenever it finds the symbol ” (except if it’s being used in HTML) change it in the first instance to “ and in the second instance to ‘ ‘ as one step in the process of turning the input code into ps or pdf. I’d do it myself but I don’t know any programming languages.

here?: “There are 27 objects”

here?: “one of the objects has value 27″

Ian: That depends a little on regional typographic styles. I think in European countries it is commonly not italicized, in American typography it is, however.

When I wrote my first book in LaTeX (The Logic of Typed Feature Structures), the good folks at Cambridge University Press gave me a clinic on typesetting, with everything from kerning to laying out bottoms of spreads to be even. Once you learn more about typesetting, almost everything out there looks terrible. Especially egregious is all the wasted white space in most docs, especially vertically; CUP’s LaTeX cleanup crew actually reduced the length of my book substantially by tightening everything up.

Integrals should be written as “\int_0^1f(x)\,\mathrm{d}x” for the d to be not italics.

I have my students write in Latex all the time. If I had to come up with my own list of mistakes my students make all the time I would definitely have included (3) and (4).

Two others that I would add are to use the letter x instead of \times, and the dual to your (4)—writing text in math mode. For example, \{x\in S: x>2 and x<4\} (the "and" should be plain text).

About differentials, aside the \, spacing, I prefer to write the d uptight, so I usually define a \newcoomand{\ud}{\mathrm{d}} and use it whenever I need a differential.

A better way is to use real curly quotes. On the mac US keyboard layout, they’re option-[ and option-shift=[ (single quotes are under ]). I haven’t used windows in a while but the US-International keyboard layout used to be almost as usable as the mac layout.

If you use Emacs, AUCTeX lets you use the inch-mark ” just as you would in word-processing software and contextually switches it to “ before text and ” after (” with a second press if you are talking about inches). The config group tex-quote lets you configure this behavior and more. The csquotes package is helpful if you use different languages with different quoting habits – your source can contain “” and the result in French for example be typeset using «».

Is there any other TeX-authoring software that does this?

I also recommend aligning LaTeX delimiters vertically, the way one would when writing C code, especially for delimiters like \left( and \right) that might have a lot of content inside.

I also am repeatedly guilty of forgetting to close off an environment properly, such as when I have nested enumerate environments (happens a lot to teachers who do this sort of thing for creating tests).