The principles set out in 'Ximenes on the Art of the Crossword' have further evolved in the 53 years since they were first established, and they form (with a few minor variations) the standards for the diagram construction and clueing seen in barred crosswords published in the UK (in particular the Listener, Azed and Mephisto series, and puzzles appearing in the Magpie magazine). In essence, the goal is to achieve fairness to the solver (which was, and some would say still is, often lacking in 'libertarian' crosswords) whilst not depriving the setter of the means to deceive.
A maxim frequently quoted is that of Ximenes' predecessor, Afrit, who wrote: "I need not mean what I say, but I must say what I mean." In other words, a clue as a whole can superficially appear to mean one thing but, when read another way, can have a sound cryptic interpretation which is entirely different.
It has long been accepted that punctuation separating the wordplay and the definition is not essential. Beyond that, Ximenes' view was that punctuation which was - strictly speaking - necessary to the cryptic interpretation could reasonably be omitted, but that the introduction of misleading punctuation was unfair to the solver. However, I believe that he was referring specifically to marks which introduce confusing pauses or breaks. In his book 'The A-Z of Crosswords', Jonathan Crowther (Azed, whom many consider the heir of Ximenes) wrote: 'If there is a comma in a clue, but the cryptic reading of the clue only works without it being there, the setter is taking unwarranted liberties and not playing fair by solvers. Similarly a hyphen between parts of a word binds the two parts into a single compound unit. Expecting solvers to treat this unit as two separate words in order for the clue to work is also unfair." So 'second-best' could not constitute the wordplay for STOP, for instance.
I can't, however, think of a situation where the inclusion or omission of quotation marks would be considered even by the 'non-libertarians' among us to be unfair to the solver.