Monk's cardboard tree shifts positions from the back left corner when looking straight at it to the middle of the room when shown from the back.
As Monk first approaches "Brother Leland," the edge of the hood of Stottlemeyer's robe is folded. Then it's folded differently, and unfolded as the camera changes angles.
When Monk and Julie are talking in the living room, her arms suddenly change position between shots. From behind they are crossed but from the front they are by her sides.
The people who drank the water would stop taking their medicine, thus their symptoms would reappear, thus proving the water didn't cure them.
Owen was afraid that with the renovation the body under the fountain would be found, which leads to the question why the body wasn't found when they erected the fountain.