While Jessica is walking in the garden and talking to people after the will video has been viewed, the lapels of her blouse are over her jacket or tucked under it in successive cuts spanning some minutes.
While the film is set in Ireland, the Garda (police) cars have Northern Irish registration plates (PIB XXX).
While arriving at Rose Cottage Jessica Fletcher is wearing only a woollen suit
jacket, later when she sees Nora peering through the window she puts on her waterproof coat which she didn't arrive with.
It is correct that Jessica did not arrive at Rose Cottage with a raincoat but the raincoat can clearly be seen on the hook beside the door when she enters the cottage. It is obviously left there by someone else or even belongs to Breeta (who is already at the cottage before Jessica). Jessica merely borrows the raincoat before she departs from the cottage in search of Nora and therefore is not really a revealing mistake.
"It's just lines," says Breeta, when looking at her clue. While she correctly identifies Ogham later, someone who studies Celtic myths, legends, and history as Breeta does would more than likely instantly recognize this distinctive system of writing.