Revealing mistake: When Nick is in the shed in the desert, sunlight is coming in through hundreds of holes in the walls and roof. Since the sun is in one spot, all beams of light should be in the general same direction. In this scene they come from at least 5 different directions, with some originating from a light source very close to the outer wall (causing beams in a radial pattern).
Other mistake: Season 10, episode 4 "Coup de Grace": When Nick is doing the phenolphthalein test on the q-tip, it turns pink immediately and starts to overflow pink coloring all the way down the side of the stick, which is not how that test works. Normally it takes a few seconds and only turns color around where the blood is.
Continuity mistake: Near the start, when Ray is showing the photograph of Madeline with the security guard to passersby asking if they've seen her and also when he shows it to Nick, we can see the photo Ray is holding out in the wide shots, but in the two closeups of the photograph it's actually a different photo. Then later, when Ray shows the photo to Madeline's mother it's the same as the one from the closeup earlier.