The first vague concept: abuse of process
Complicity by Australian officials in the unlawful deportation of the defendant (appellant) to Australia led to subsequent criminal proceedings against the defendant in Australia being stayed as an abuse of process in Moti v R  HCA 50 (7 December 2011).
Abuse of process is open-ended, not to be confined to rigid categories of official misconduct (60):
Recognition of abuse of process is a response to the policy of even-handed justice and the maintenance of public confidence in judicial process.
Heydon J delivered an interesting dissent, focused on difficulties arising from the vague concepts concerning abuse of process and its lack of definition. Among the points he makes is the availability of alternative, disciplinary, responses to official misconduct instead of giving a person who may be guilty of serious offending immunity from conviction.
There are also some observations in this case on payment of prosecution witnesses, which was another ground of this appeal but which did not need to be considered in detail as no impropriety in that regard was held, unanimously, to have occurred.
The second vague concept: miscarriage of justice
In Handlen v R; Paddison v R  HCA 51 (8 December 2011) the High Court held that the proviso could not be applied where a trial had proceeded on a mistaken appreciation of how participation in the offending could be proved. The requirements for secondary liability, namely that each appellant had intentionally aided, abetted, incited, counselled or procured the commission of the offence, should have been applied. (An alternative form of secondary liability was not relevant in this case.) But the trial proceeded wrongly on the basis that proof of membership of a joint criminal enterprise would be sufficient if commission of the relevant offence was part of that enterprise. The error is that not every member of such an enterprise is necessarily a party to every offence committed by members of the enterprise. This was overlooked by all counsel and by the trial judge. The Court of Appeal of the Supreme Court of Queensland had recognised the error but had applied the proviso because it was satisfied that the appellants were guilty, and there had not been a departure from the fundamental requirement of a trial according to law.
The majority ordered a new trial, Heydon J dissented and would have dismissed the appeals. He analysed the evidence and found guilt proved regardless of how the trial had been conducted. He did not see the defects as fundamental. For the majority, regardless of the strength of the evidence the trial had been such a departure from what was in accordance with the law that, in effect, the right to a fair trial was the dominant consideration.
Vague concepts can still be useful in the law. Reasonableness, fairness, interests of justice, the public interest, the weighing of values underlying rights, do not need to be defined as if they were mathematical concepts. Numbers too, when used in measurements, involve margins of error and require probabilistic reasoning. These areas of vagueness are opportunities for the exercise of judgment. Complaints about vagueness are like the formalists' complaints about pragmatism.
An unruly heckler at the back of the room might cry out that Heydon J had, in the first of these appeals, been too much the formalist, while in the second he had been too much the pragmatist.