The reasons for the appeal being disallowed have not been published because there is an active case - that of a retrial into the count on which the jury couldn’t reach a verdict. It’s normal, and in contempt, for any information to be published that poses a substantial risk of serious prejudice when a case is active.
As for the New Yorker article, it relies heavily on some inadmissible information and witness evidence.
Before every trial, the information that will be presented to the court is collated and sorted and reams and reams of it are not used. Some is ruled inadmissible by the judge because it is prejudicial. This is normal. If every piece of paper or every word of every statement was presented to the jury, every trial would take years.
The problem with the New Yorker is that it places great emphasis on the evidence that is in Letby’s favour, and none of that which might reinforce her guilt.
Jury trials hear the prosecution and defence case, and so often after the prosecution has made its case I am certain of guilt (I spend my working life in courts as a layperson). But then the defence presents their evidence and it’s a balancing act for a jury rather than any silver bullet piece of evidence that proves something 100 per cent.
The New Yorker is trying to prove its own hypothesis rather than providing a balanced view. That’s ok - it’s a newspaper not a courtroom - but it’s also why someone’s guilt should never be decided by people who were not in the courtroom and have reached their view solely through media coverage (even when that coverage has been excellent, and the Letby trial was an example of excellence).
I did sit through a very small portion of the Letby trial and it was so diligently and carefully argued. It’s highly unlikely a jury would reach an incorrect verdict in such a long and detailed trial.