Continuity mistake: When the psychic collapses, sun is streaming through the window, indicating early afternoon. When we see the ambulance driving away a few scenes later, it's dark outside. It's highly unlikely it took a medic team several hours to get there and stabilise her.
Factual error: Scully reads to Mulder from a book all about flukes (Trematodes). However, the information she is quoting is wrong. She states that flukes or flatworms have a "scolex" with hooks and suckers. These are actually the distinguishing characteristic of cestodes (tapeworms). Trematodes have no scolex and definitely no hooks.
Continuity mistake: After the part where the head Kindred woman tells Mulder and Scully "I asked you not to interfere", Mulder leads Scully away. From one camera angle, he is leading her away by the hand. In the same scene, but from a different camera angle, he has his arm around her. When we go back to the first camera angle, he is once again leading her away by the hand.