Tom rights the victim's chair when he tries to recreate the scene. The next time he returns to the scene with Jane, the chair is upended on the floor again.
Not only is the chair in the farmhouse lying down on Barnaby's second visit(after he had stood it back up the first visit), there's blood on it the second time. It was clean the first time.
When they show the death thought to be a suicide with a rigged gun in the first scene, the character yells out loudly right before he is shot. When they show the same scene in a flashback, he does not yell. While this could be considered to be a mistake, it is a flashback from the point of view of someone not in attendance at the shooting. They would not suggest that he might shout out.
Odd that DCI Barnaby drives onto the field of play at the cricket match - the plastic flag boundary markers are visible behind his vehicle. The cup of tea he is given is drugged and after getting back into his car, with the match going on, he passes out in the driver's seat. Apparently no one at the match minded that a car was parked on the pitch with the driver unconscious. When Barnaby regains consciousness it's dark and (nearly) everyone has left the club ground.
After almost being choked to death, Dr. Jane Moore mentions, upon hearing of another death, "well that makes 4 murders". At this point, there had only been three.