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: The episode on CSI:NY was called "Love Runs Cold" and first aired on October 4, 2006 (Season 3, Episode 3) and involves the investigation of a model found stabbed to death by an ice dagger.
OneHappyHusky