I don't think it's possible to come up with strict, let alone unambiguous, answers to your questions. (And, I don't think you're asking for such guidelines...)
An important general aspect of what's considered to be good typography is the creation of an even amount of "color" -- or "average grayness", if you prefer -- across pages and across paragraphs within a page. There are obviously many factors -- so far unspecified -- that determine a page's "average grayness". E.g., are the paragraphs on average quite long or quite short? How tight is the interline spacing? Are successive paragraphs separated by extra whitespace? Are there lots of displayed equations? Taken together, these aspects should indicate fairly clearly when (and when not) to use \frac and friends in inline math situations.
One of these aspects is whether running text is set single-spaced or more loosely. Obviously, the larger the distance between successive lines of text, the less deleterious the effect of using \frac -- as well as exponents, subscripts and superscripts, and anything else (such as integral, sum, and product symbols!) that rises above or falls below the space defined by the baseline and the caps-line will be on the average color of the page. If the text is set single-spaced (and especially if the baseline skip is modest, say, 20% more than the font's nominal size), almost anything that rises above the capsline or falls noticeably below the baseline risks forcing the use of extra space between lines to avoid collisions -- and should thus be used sparingly at most in inline material.
Incidentally, having to increase the baseline skip for just one line is exactly what happens because of the (clearly deliberately undertaken) use of \frac in the first paragraph on p. 19 of the document you've cited in your posting:
Observe that the space between the second and third line is quite a bit larger than the other spaces in the paragraph.
To sum up, publications (including working papers) that are typeset single-spaced should probably avoid having \frac (let alone \dfrac!) appear in running text. In contrast, if the working paper is set with one-and-one-half-spacing or (shudder) double-spacing, use of \frac is going to be much less problematic from the point of view of creating even typographic color. Some design purists might go as far as saying that double-spacing has already killed off any chance of creating good color. If color is already hopelessly compromised, any extra damage done by occurrences of \frac or \dfrac in double-spaced text may be minor, right?!
Well-designed publications should take into account whether there's a need to have significant amounts of inline math material. For instance, for the book Concrete Mathematics by Graham, Knuth, and Patashnik, a conscious decision was made to choose a baseline skip of 13pt rather than the more standard 12pt. This was done, in part, to accommodate the use of subscripts, superscripts, etc in the running text. If I remember correctly, a second reason for choosing a looser-than-normal baseline skip was that the font used for the book, "Concrete Roman", was felt to be a bit dark if employed at a more standard baseline skip of 12pt. Widening the baseline skip a touch was felt to bring about a better "average color" -- regardless of how much inline math material was present in a given paragraph. Clearly, whatever may constitute "optimal" color comes with a high degree of subjectivity. Equally clearly, I don't think there's anything wrong with having this degree of subjectivity.
Best Answer
What's better from a typographic point of view -- inline-style fractions or display-style fractions while in display-math mode -- depends crucially on the contents of the fractional terms.
For the two examples at hand, I can see nothing wrong with using inline-math notation, shown on the right-hand side of the two rows below.
Incidentally, I'd say that
\left( \frac{1}{t}\right)^{3/2}is less than perfect, typographically speaking, not because of the presence of the fractional term\frac{1}{t}but because there's too much whitespace between\left( \frac{1}{t}\right)and the exponent (3/2). If you must use these large round parentheses, you should probably writei.e., insert a negative thinspace before
3/2, in order to "snug up" the exponent material to the closing parenthesis.