My problem with the "bigger picture" is that as soon as you start to look at any part of it in detail, the evidence doesn't hold up very well. For example, the handover notes - if the argument is that she shouldn't have had them and therefore was breaking rules then yes that's something against her character, but it doesn't indicate that she caused harm to anyone. If the argument is that they were kept as trophies then it doesn't stand up. There were over 200 handover notes but only 21 related to the babies she's convicted of harming and 4 of those babies weren't mentioned at all. They were generally stuffed in bags (apart from her first one) not carefully preserved. They were also her own notes, not something belonging to the babies or their families. If they're trophies then they're not very good ones.
Googling/Facebook searches of the parents. If you're arguing that she shouldn't look up things related to patients on the internet then maybe it's unprofessional, but it's information that they themselves have made public. If it was looking up private or medical information then that would be criminal in itself. There's also the scale here - 31 searches related to the families against a total over over 2200 in the period. To me that seems like poor evidence of "obsession".
The "confessions" scribbled on post it notes also contain a lot saying that she's scared or innocent, which also seems very cherry picked to me.
I think the number of cases she was charged with are also supposed to indicate that she must have done something to be accused of so many things but to me that indicates weak evidence, not strong. The fact that the incidents were not seen as suspicous at the time but only found after a trawl through notes and they cover a range of supposed harms including insulin poisoning (including a time when she wasn't present), injury to liver (how?), overfeeding with milk (never before seen as an attempt at murder) seems more like throwing anything and everything at the wall to see what sticks.
If we're looking for a pattern that matches "serial killer" - trophies, moving around if suspicion falls on them, escalating behaviour, developing m.o. then I don't think it meets the standard.
Whatever you look at it always seems that somehow it's supposed to be the volume of weak indications that should be convincing. There's also never any comparison with anyone else either. Presumably if someone else had been accused then there would have been a whole other set of behaviours that would be considered suspicious. Can we determine whether someone has commited a crime based on their other behaviour?
Given enough time to pick through someone's character and possessions (and they had a lot), I think you'd expect to find much clearer evidence of wrongdoing even before you get to the medical evidence if that's what you're considering as circumstantial evidence.
There's no clarity on how events were selected as "suspicious" or not and "unexpected" is a bit subjective. By not looking at the maternity notes and not allowing consideration of other comparable babies (e.g. baby Y the other "insulin" case) and the selective rota chart used showing that she was "always there", I think they built a case that made it seem like that the ones she was charged with (and only those) were definitely deliberate harm.
There are an awful lot of qualified and credible people who have come along since who say that you can't treat statistics like that and that the evidence of deliberate harm is shaky.
None of this is to say that she's definitely innocent, only that there is some serious doubt as to the evidence presented in the trial. Even if she's guilty as charged, the fact that she's been found guilty in this way means that innocent people could also be convicted and that's worrying.