After the death of David Farmer, there is a scene with Dr. Parr, DCI Barnaby, and Harriet Farmer. Harriet - a year-long coma patient with an obvious tracheotomy at the beginning of the episode - shows no sign of even the faintest scar at this point. This sort of wound would leave a scar even years later.
When some chess games are written in notation on some clear boards in the police station, the annotation is inconsistent with some of the moves having valid notation and some not. For example Q x bb is shown in several shots.
Kate says there were fragments of the murder weapon in the wound. A steel blade will not leave fragments when cutting through flesh. To chip away material, the material being cut must be able scrape away material, and soft flesh cannot do that with hardened steel.
Whenever Harriet Farmer is attacked in the woods, she bleeds where struck on the left side of her forehead. A year later whenever DCI Barnaby opens the case file while riding in the car, Harriet's photographs show her bloody injury on the right side of her forehead.