Generally speaking, two steps are involved: first, assessing the credibility - or reliability  - of the witness's testimony ("This is the hammer I lent the defendant"), and second, if it is sufficiently credible to satisfy the fact-finder that it is true, the assessment of its probative value on an issue in the case. There is not necessarily a standard of proof for deciding whether testimony is credible, although it is often said that if the evidence must be accepted before a verdict of guilty can be returned then the credibility of that item of evidence must be established beyond reasonable doubt. For less central testimony it is likely that credibility need only be established to a level that "satisfies" the fact-finder that it is true, and here satisfies means on the balance of probabilities. However, this is a rather vexed topic and jurisdictions may differ in how they express the requirement for acceptance of the truth of evidence.
Credibility and probative value are matters specific to the particular testimony that is being considered, but when it comes to assessing the verdict on the accepted evidence, it is all the accepted evidence that must be taken into account. This is why the court can say it is wrong to latch on to one item of evidence and claim that it creates a reasonable doubt about the defendant's guilt. There will be occasions where that can be done, for example if an alibi is accepted notwithstanding that the other evidence strongly supports an inference of guilt. But other than alibi evidence, and also evidence supporting an affirmative defence (where the defendant's actus reus and mens rea are not disputed), in most cases, including Fennell, all the accepted evidence must be considered in deciding whether guilt has been proved beyond reasonable doubt.
But that’s not all. References by the High Court of Australia in Fennell to Bingham remind us of how Lord Bingham, delivering the judgment of the Privy Council, analysed our notorious circumstantial evidence case, Bain v R  UKPC 33 (10 May 2007), noted here. But the Bain appeal was different insofar as it involved fresh evidence which called into question whether the combined effect of the circumstantial evidence would, in its light, be sufficient to support a verdict of guilty. As there was fresh evidence, it was appropriate to order a retrial. It was not for the appellate court to itself come to a verdict on the new evidence. In contrast, Fennell was not a fresh evidence case. The prosecution relied on categories of evidence - alleged theft, alleged motive, alleged possession of the murder weapon, and alleged opportunity - and each was shown to be unreliable. This was a case of absence of reliable evidence, not a case of assessing on an overall view the probative value of reliable evidence. On finding the conviction unsound the Court could order an acquittal.
 In New Zealand s 28 of the Evidence Act 2006 is relevant where the reliability of a defendant's statement is being considered, and this has been interpreted as meaning that the truthfulness of the evidence can be relevant to assessing its reliability, a position not criticised by the Law Commission in its Second Review of the Evidence Act 2006, NZLC R142 at [6.19]-[6.23]. In R v Wichman  NZSC 198 at  the majority in its joint judgment observed in relation to the possibilities that someone who is innocent may be convicted on evidence which turns out not to have been reliable, that these risks "... are inherent in the criminal trial process and cannot be completely avoided. They can, however, be mitigated in various ways; in particular by recognising the risk of unreliability; the provision of a reliability screening process to be carried out by the judge; judicial warnings; jury assessment and the rules as to the burden and standard of proof."