Another child, child E, was found by his mother bleeding profusely from his mouth, with Letby in the room at the time. She brushed it aside as being caused by his feeding tube. Letby and the mother disagree about various timings of conversations that night, which was used as proof that Letby had been lying (since the mother had records of when she made various phone calls).
Beyond that is where it gets a lot more speculative.
She took a lot of material relating to the babies she looked after home and kept it around the house, including medical records and weird stuff like blood gas readings which she may have fished out of a bin. Some of this material relating to babies she was accused of killing/harming, but there was also material relating to other babies. A serial killer's trophies, or just someone with poor boundaries and no concept of data protection?
She looked up a lot of people she met on Facebook all the time, including the parents of some of the dead babies. Colleagues also noticed she was always around when some of these parents were grieving having just lost their children, and offering to do things like make prints of their feet, memory boxes and so on. Caring nurse or grief vampire? She was on holiday and a nurse texted her to tell her that triplets had been born on the ward. She texted back that she would be 'back with a bang then'. Later, two of the triplets died. Does that mean anything?
After she was accused she wrote a series of rambling notes which included the phrase 'I am evil, I did this' but also 'I haven't done anything wrong'. A confession, or the ramblings of someone going through a breakdown?
There were also suggestions that she was trying to impress a married doctor she fancied.
Some of the consultants (not just 1 - I think maybe 4) on the ward suspected her, largely because she was present for each of the deaths. They tried to get her removed from the unit but encountered resistance from management and in the end had to write her a letter of apology. I think the nursing staff were more split on her guilt or innocence.
The defence tried to argue that there was no conclusive medical evidence that any of these deaths were caused by foul play. They also heard testimony from a plumber that the plumbing in the hospital had major problems and that sewage-contaminated water would sometimes spurt back into the bathrooms, thus possibly a source of infection which could threaten these vulnerable babies. The defence didn't call any of their own medical experts, I'm really not sure why - this looks like a very bad choice on their part.
Most or all of this evidence is circumstantial, but the judge specified that the jury would be permitted to allow it all to build up into a picture.
As I said, I thought that the insulin readings probably proved some form of malicious actor (which couldn't really be anyone but Letby) but now that those findings have been challenged I'm rapidly coming round to the view that the conviction is not safe