Plot hole: In the lab when Liz makes the slides of her cheek cells and the cells from Max's pencil, the first time she doesn't add stain and the second time she does. If she's going to be a molecular biologist she really ought to learn to apply techniques consistently. (00:07:30)
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.
Plot hole: Sydney is able to surmise from the artwork (we could also say from the writing, but her rival is one step ahead of her for 2/3 of the episode and it is established that he does not know the language) the precise location of the koi in Lumbini. The map is 150 years old, but there's no way even with a big stretch of imagination to buy that they both'd be able to pinpoint with such ease and certainty its location in the basement of a random building in the bustling market center of a town, that surely changed plenty during the past century and that does not bear any special landmark.