Other mistake: The animation of the video player is a static image since the graphics don't move, and since it's a live stream it shouldn't have the pointer at half of the screen in the first place. (00:21:50)
Continuity mistake: When Amaro and Benson are searching the hotel room, they both put on gloves as they enter (Amaro puts gloves on both hands, Benson just on her right). After Amaro says "they weren't after cash", the camera pans back to Benson who is no longer wearing gloves, but holding one in her right hand and using it to pick up items. The camera pans back to Amaro who opens a safe and finds a passport, still wearing both gloves. He opens the passport and recites information, and we see Benson now wearing her right glove again. We then go to a POV shot of Amaro and he is reading the passport with no gloves, before the camera immediately changes shot and he has them both back on again.
Plot hole: Although William Lewis burns his fingertips in an attempt to avoid identification, the Special Victims Unit could have identified him early on by examining the remaining unburned area of Lewis' hands, and in good police procedure still record the newly scarred fingerprints, as these new scars actually make his fingerprints more unique. His scarred fingerprints would still be at Alice's apartment crime scene, and during the trial at the end of the episode the prosecution would still have a strong argument for placing Lewis at Alice's apartment, even if the DNA evidence is thrown out because of alleged cross contamination.
Other mistake: The birth dates of the sisters have been switched as Rollins looks on her laptop. (00:10:30)
Answer: It was a misconception about Jehovah's Witnesses beliefs. Only blood transfusions are discouraged in their beliefs, medically.