While Hotch, Prentiss, and Morgan are talking to Viper after his class, the top earring on his left ear is flipped up in some shots, but laying correctly in others.
Mixing Bleach and Ammonia produces toxic gas.
Towards the end of the episode, it shows the unsub's mother being on dialysis. Dialysis needles do not get placed in the top of the hand, they are placed either in the forearm or the upper arm. There are also two needles associated with having dialysis done, not just one.
The episode is set in Atlanta GA. At the home of Vanessa's family there's a Cadillac in the driveway with a GA tag on the front. GA has never had front tags.
The unsub uses a roll of tape to cover the victims mouth and then drops the roll into the bucket of cleaning solution. The thunk it makes shows the bucket is empty.
The newspaper article has a typo in it. It says "Take my class and learn how to 'uinlock' desire."