When is an error at trial insufficient to require an appeal court to quash a conviction?
The more the attention that is given to this question, the more difficult it is to answer. At least, that was the experience of appeal courts in the 2000s. Before then this question had gone largely unexamined, and appeals were decided with appellate courts deciding apparently intuitively whether miscarriages of justice were substantial enough to require the quashing of convictions.
I have considered this in discussing Weiss v The Queen  HCA 81 on 16 January 2006, and see also the discussion of Grant v R (Jamaica)  UKPC 2 on 20 January 2006. A difficulty was when should the appeal court act like a jury and consider the evidence and dismiss an appeal because despite the error at trial the evidence was sufficient to convict? See Bain v R (New Zealand)  UKPC 33, discussed here on 11 May 2007.
The Weiss approach has been followed with minor adjustment in New Zealand: Matenga v R  NZSC 18, discussed here on 9 July 2009.
An unattractive aspect of the Weiss approach is that it seemed to say that the appellate court may dismiss an appeal notwithstanding an error at trial if it considers that the evidence was sufficient to support a conviction. Obviously the ends (conviction of a person who is plainly guilty) cannot justify the means (never mind whether the trial was fair). To avoid that unpleasantness two requirements had to be met before a conviction could be upheld: the trial had to have been fair notwithstanding the error, and the evidence of guilt had to have been sufficient.
So, when does an error not affect the fairness of the trial? It is difficult to generalise without a definition of "fair trial". I tirelessly suggest one here.
Yesterday the High Court of Australia dealt with an appeal in which the errors at trial had been so substantial that it was unnecessary, indeed impossible, for the Court to address the sufficiency of the evidence: Patel v The Queen  HCA 29 (24 August 2012). The appeal was allowed because no weight could be given to the verdict, the jury were overwhelmed by the prejudice created by the admission of evidence that, because of a change in the prosecution case, was inadmissible, and the proviso didn't apply: joint judgment of French CJ, Hayne, Kiefel and Bell JJ at -. Heydon J separately agreed, holding at  that there had been a departure from the requirements of a fair trial to such an extent that the court could not justly assess the strength of the case against the appellant, applying Gleeson CJ in Nudd v The Queen  HCA 9, discussed here on 9 March 2006.
This seems to me to be a case where the unfairness was the rendering of the jury partial – that is, not impartial – through the introduction of evidence that would prejudice its judgment against the defendant.
Heydon J noted two difficult questions that did not have to be answered in this appeal : to what extent should a judge disallow the introduction of evidence although no party objects to it, and when should a judge require the prosecution to provide particulars although they were not sought by the defence?
I suggest the answer to those is indicated by the meaning of a fair trial. But until judges get down to explaining what a fair trial means we are left to define it for ourselves.
I should add that in New Zealand we have revised the conviction appeal criterion by abolishing the proviso and defining miscarriage of justice to include errors that result in unfair trials: Criminal Procedure Act 2011, s 232 (not yet in force). Again, there is no definition of fair trial.