When Sgt Howie is unable to start the plane, he calls the harbor master. While the harbor master is rowing back he calls out to Sgt Howie "What's the matter, won't she go?" Notice that when he begins this question he is nowhere near the plane, but as he is finishing the question, he is now alongside the plane.
While Sgt Howie is at the chemist shop he shows Lennox (who is mixing something with a mortar and pestle) a photo of the missing girl. Notice how in between shots the photo goes from Howie's hand into Lennox's hand, without having been handed over.
In the scene where Sgt Howie is in the classroom, he places the blackboard duster at an angle on the desk lid where Miss Rose sits, later when he goes to open the desk lid the blackboard duster is now level at the top the desk.
When Sgt Howie inspects the school register he stops on "Belthane Term", where Rowan Morrison's address is given as "The Tuck Shop." The shot changes to a close-up, and his finger runs along the same page to now find she was resident at "The Post Office." His hand is also clearly in the wrong position on the following change.
In the scene where Howie questions the Doctor about Rowan Morrison's death certificate, the Doctor is seen to open his front door and step partly inside. The shot cuts away, and when it cuts back to the Doctor his front door is shut. He opens it again and goes in.
The calendar in the Photographer's shows May Day to be a Tuesday, therefore Sergeant Howie flew out on Sunday. Not only is this notably unlikely for a routine police investigation in the generally religious Scottish Highlands, The Director's Cut shows Howie receiving the letter on the same day. There were no Sunday postal deliveries at the time.
Most of the "naked" girls dancing in the stone circle and jumping over the fire are wearing flesh-colored body stockings (the film was shot in autumn and not in spring as it was set, and thus was very cold).
In the scene where Sgt Howie hits McGregor (who is dressed as Punch) with a candlestick, watch closely and you can see that the blow from Howie is aimed into the padded section on the back of the punch costume, rather than at the back of McGregor's head.