At the beginning of the episode, the Inspector is describing possible suspects and their special skills - one of whom is a seasoned hitman, one of whom is martial arts expert. The third, he warns, is a suicide bomber. How could he possibly know this? Suicide bombers don't exactly make a career of it - it's a strictly one-time event!
The murder itself, when the coroner is examining the body is still believed to be a stabbing. She mentions that the weapon went through the heart and is 'barely a millimetre' in width. This is patently not true, as we see once the weapon is revealed as a spike. Presumably, the writer meant barely a centimetre, since a millimetre would almost make even a needle out of the question as a weapon.
*** Spoilers ahead ***
The setup for the murder is not very smart, and it is actually very unlikely to kill someone like this. In order to kill, the victim should make contact not only with an electrode - the clock, or the pins in case of the Redcap - but also make another contact with either another electrode or ground. In the Redcap, that may have been some metal radiator. But in the case of the judge there is no electrode or ground: his bed is made of wood which is non-conductive. His mattress might have been conductive if it was a very poor quality box-spring - unlikely for a man of his standing - but even so, it is placed in a wooden bed. At most he might have felt a little tingle or a prick when his arm had brushed the bed table, thus making a circuit. But this would certainly not have killed him, nor even stunned him enough to be stabbed without resisting.
There is a major mistake in plotting in this storyline. As we discover, the suicide of Duncan Proctor was nothing of the sort. They explain away the ambulance coming as some friends doing a prank. But a whole house full of guests has just seen or known about a guy jumping to his death from a high balcony. Why was there no police report? The police would have had to be involved at some point in a suspicious death. It's even down to Maddy to discover that there was no hospital admission or anything of the sort, when the police are now involved in the murder of Felicity, and would presumably have access to that kind of information.
As his wife is making him a nettle sandwich, Sylvester LeFley is on a sunlounger, on his front, having his legs massaged. His wife is watching him. She turns to walk the few paces to him, proffers the plate and he is suddenly miraculously on his back now, looking up at her.
When Maddy says she's going to have a 'shufty' round Norman's room, she hands Antonia an uncooked chicken to "get the lunch on." She goes upstairs, looks in his wardrobe, then in his laundry basket, finding him in the bath, and gives up, going back downstairs, by which time not only is the chicken cooked and ready to carve, but all the vegetables are cooked too. It's feasible that Maddy might have spent a few more minutes looking round upstairs, but a raw chicken and roast potatoes would take a lot longer to cook!
At the end of the episode when we see Emma Lazarus's stalker with a box, which we know contains her head, he's sitting on a plane back to America and is told to put the box in the overhead compartment. Even given this was before the major security enhancements, all hand luggage was still x-rayed. It would take a particularly terrible security officer not to spot a severed head in a box!