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: In the first scene when we see Dr Langston from behind as he's watching people passing by he's wearing glasses but when we see his face he's not wearing any. (00:00:15)
Answer: He doesn't have the authority to arrest him - when anyone is arrested in the show, a police officer does it. Also he tells Ty that he is going to be submitting his case findings to Ty's insurance company, who would no doubt contact the IRS, who then would have him arrested for fraud etc.