When Barnaby and Jones are questioning Lesley and Barbara Flux in their garden, as they deny being murderers, Lesley puts his arm around Barbara and pulls her close. And then does exactly the same thing again in response to Barnaby's immediate next question, having apparently dropped his arm and moved away from her again in only a few words.
When Giles Cato sneaks up on Gerry Moore's pickup to take some photos, he goes into the woods to take the photos from the side, but the freeze-framed shots that represent his photos are taken from exactly the same camera angle as the shot that showed him moving up the lane and going into the woods, rather than from within the woods.
(At about 59:00) When Barnaby visits the solicitors' offices, the brass plaque says "27 Main Street", yet there is a number "21" prominently carved on the front door.
One would expect a house implicated in a murder would be swarming with police and forensic experts, cordoned off and exhaustively trawled for evidence. However, this would render the rest of the plot impossible, and so it doesn't happen.