Revealing mistake: When Agent Hotchner receives a text from JJ while interviewing the suspect, it is actually a screenshot. You can see Camera Roll in the upper left hand corner, "2 of 2" where JJ's name should be, and the Share/Play/Delete banner at the bottom. It is covered by Agent Hotchner quickly tapping on the screen to clear the banners.
Continuity mistake: In the scene where you first watch the killer drain a victim's blood, the upper part of the glass jar is coated with blood, but when he puts it in the fridge this part of the jar is clear. On the other hand some of the jars in the fridge are still fully coated with blood, which shouldn't be as the blood had the time to gather at the bottom.
Character mistake: When Reid realizes who the unsub is, he asks Hotch if he was introduced as "Doctor" or "Agent". As explained in the pilot (and in every episode since), the team has always introduced Reid as "Doctor", to make sure that the people they meet treat him with respect and don't just see him as a kid.