When the third victim is killed by being impaled with a pike, the weapon passes completely through the victim's torso from back to front, ending up with the blade entirely visible outside the victim's chest. However when the murder is shown again in flashback during the killer's confession, the blade only penetrates halfway into the victim's back and remains there.
The first murder victim is killed by being buried alive under a large amount of dirt and soil in a hole at an archaeological dig. However, when her body is shown on the mortuary slab, a close-up of her hair shows it is perfectly clean.
The first priority on that dig would have been getting the full skeleton to the lab for radiocarbon dating. The second would be examining the bones in the church for the same.
Barnaby told Zoe's lover he was the last person to see her alive. This is untrue. That would have been the backhoe operator who buried her alive.