The jury system, while not perfect, is much better in reality than the UK version of this programme suggests. It's still flawed, but alternatives like an all judge panel I believe would be worse.
The Judge should have been shown giving a detailed summing up of the evidence and clear instructions to the jury. For example he should have explained the very specific grounds they might convict the accused of manslaughter rather than murder.
These grounds would NOT include using it as a handy compromise if the jury is split between murder and acquittal!
Plus, it is usually required that the jury waits until after the Judge's summing up & instructions before discussing the evidence amongst themselves. And the full jury must be present in these discussions, there can be no private chats in small groups!
I believe that the current UK jury system would greatly benefit from adding professional facilitators. A facilitator would join the jury only once it has retired to reach a verdict. He/she would not be able to offer any opinions, but would help with the practical process of how to reach a consensus.
For example, if the jury are unsure on a point of law, the facilitator can remind them that they can put written Qs to the judge. Or the facilitator could suggest everyone reads the Judge's instructions again if they appear to be ignoring them or getting lost in the weeds!
Such a job would be fascinating. And I'm sure it would make deliberations shorter and be less likely to result in a hung jury. So could save money and court time.