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.
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.