Whether failure to call evidence at trial should be grounds for quashing a conviction is an issue that often has to be decided in appeals, as it was in Taylor v The Queen (Jamaica)  UKPC 8 (14 March 2013).
Here the Board split, Lord Kerr dissenting, on the application of the law to the facts. There was no difference of opinion on what the law is.
It was unnecessary to decide whether counsel were at fault in not calling the relevant witness, because the issue is the impact of the absence of the evidence on the verdict: Lord Hope for the majority at , applying Lord Carswell in Teeluck v State of Trinidad and Tobago  UKPC 14 at , (discussed here on 1 April 2005). The test is whether, after taking all the circumstances of the trial into account, there is a real possibility of a different outcome: Taylor at . Might the evidence reasonably have affected the jury's decision to convict? The majority held that there was no reasonable possibility in this case that the jury would have arrived at a different verdict.
Lord Kerr said that the requirement of a real possibility of a different verdict signifies no more than an acceptance that one is left in doubt as to the safety of the conviction . This, he added (more obscurely), was not a matter for one side or the other to take on the burden of showing, but instead is a matter that must be decided in the round. The question of the effect of the new evidence on the safety of the verdict is for the appellate court to decide for itself; the court does not decide what effect the evidence might have had on the jury: , applying Dial v State of Trinidad and Tobago  UKPC 4 (noted here on 17 February 2005). Further, the question is not whether there was evidence on which the jury might reasonably convict, but rather whether there was evidence on which it might reasonably decline to do so: , applying Bain v The Queen (New Zealand)  UKPC 33 (discussed here on 11 May 2007).
Therefore it is in this sense, said Lord Kerr, that the question, where new evidence has come to light, is whether the evidence might reasonably have led to an acquittal . He proceeded to analyse the case and reached a different conclusion to that of the majority.
The application of this law is notoriously difficult for appellate courts, and it is not unusual to find dissenting judgments. One also finds dissents in appeals which have to consider, not the failure to call evidence at trial, but the wrongful adducing of evidence at trial. A spectacular example is Howse v R  UKPC 31, discussed here on 23 July 2005. The wrongful adducing of evidence raises the substantive question of the fairness of the trial, and the inevitability of a guilty verdict is not the touchstone, for even a guilty defendant is entitled to a fair trial.
Trial fairness is also raised by a failure to adduce evidence and we might wonder whether the criterion for quashing a conviction in such a case should be whether the absence of the evidence might have undermined the fact-finder's impartiality: could inappropriate weight have been given to critical prosecution evidence because of the absence of the evidence?