Character mistake: When Laura says that Alyssa was probably only sleeping with the doctor so he wouldn't be able to testify against her, the doctor says "She's my patient, nothing more." But she isn't his patient, her husband is.
Plot hole: When Rosemary discovers the side door to the church and a plastic knock, from an arrow, on the floor, she jumps to the conclusion that the arrow was shot from the side door. This all makes sense - this knowledge is how they catch Mr Danvers - but there are too many branches from the Yew tree to make this possible.
Other mistake: When Malcolm is found dead with an arrow in his chest, the arrow is pointing down at an angle, which means it came from someone high up, but, later, we find out it came from someone of around the same height and standing on the ground, not high up on a ladder, or on a rooftop, which it should be, to get that angle.