Patzer

DI Poole is measuring the bullet found in the garden lengthwise to determine what calibre it is. The calibre is determined by its diameter.

The Land Rover Defender the police are driving has the steering wheel on the left. If the island were British, the steering wheel would have been on the right. Note: Although on some of the islands one drives on the left, the series is filmed on Guadeloupe, where they drive on the right.

It's explained in the first episode that the island of Saint Marie is a former French overseas territory that was transferred to the British in the 1970s. This gives a basis for having a British Police officer working on the island. However, the police insignia still clearly show the French flag, the vehicles are all left-hand drive, and the car number plates all show the 'F' Euro symbol for France along with the département number for the French Overseas Department of Guadaloupe. If the island is now British, then it's highly unlikely it would still have French-registered cars. British overseas territories are not always treated as part of the UK, unlike French overseas départements, which are effectively just another part of France. In addition, the (nominally-British) police on Saint Marie sent evidence of the homicide to labs on Guadeloupe, which IS a French overseas territory; it's unlikely the British Police of Saint Marie would utilize resources of an extension of the French police.