Basically anything that can't be assessed scientifically.
It isn't proven that Sheila didn't kill herself. The pathologist has always maintained he was unable to conclude whether Sheila committed suicide or was murdered. The trial verdict was a majority 10:2 based on guilty beyond reasonable doubt.
You need to do more research on this case, I am surprised that you haven't familiarised yourself yet with the new evidence presented to the CoA in 2002.
This 'new' evidence wasn't considered in 1985/86, so was never presented to the court.
To read the evidence, go here...
https://www.bailii.org/ew/cases/EWCA/Crim/2002/2912.html And scroll down to paragraph 514, under the heading 'Prosecution application to call fresh evidence'
There are two main pieces of evidence, taken from the photographs, one from the positioning of the nightdress, and one from blood pattern analysis.
Those two pieces of evidence show that Sheila's head was propped up against the bedroom cabinet after the 2nd fatal shot.
She was however, found completely horizontal on the floor, with the gun placed on her body.
Given that she was dead and therefore immobile after the second fatal shot, she would have been unable to move herself into that horizontal position.
But the rucking up of her nightdress, backed up by blood pattern analysis, show that her dead body was moved away from the bedside cabinet, so that she was then completely horizontal on the floor.
It was probably done by grabbing her feet or ankles and pulling her body a foot or two away from the bedside cabinet, so that her head lay completely flat on the ground.
Jeremy Bamber probably did it because he felt it re-enforced the suicide scenario.
The three judges concluded the following:
That evidence in itself could have led to a conclusion of guilt quite apart from the many other matters relied upon by the prosecution at trial. Michael Turner QC, the bloke representing Bamber at the Court of Appeal, declined to apply for his own expert witness to counter this evidence, therefore confirming that Jeremy Bamber's own defence also found the evidence compelling. Don't forget, all this is funded by legal aid, so funding wasn't a problem.
This 'new' evidence shows that Sheila was murdered rather than committed suicide. It also fits perfectly with all the other evidence that collectively make it implausible that she committed the crime.
Once it is known through evidence that Sheila was murdered, it then means that Jeremy Bamber lied about his sister going berserk with the gun in his phone call to Chelmsford police.
It therefore becomes evident that the phone call was a clumsy attempt to provide himself with an alibi. What it actually does, is to provide direct evidence that Jeremy new what was going on in the house that night.
Once you consider the evidence, only two plausible scenarios remain. One, that Jeremy Bamber killed his family. Two, that Jeremy Bamber hired an assassin to kill his family.
They are the only two possible scenarios.
This isn't about whether Sheila did it, or Jeremy did it. Legally it is, because Jeremy Bamber personally insists on these two scenarios, which is one of his many downfalls.
In reality though, this is about whether Jeremy Bamber carried out the murders himself, or did he hire an assassin?
Given Jeremy's refusal to entertain the assassin scenario, together with his 36 year long obsession with blaming Sheila, as well as the absence of any evidence to the contrary, Jeremy Bamber is the killer.
It's a slam dunk.