The damage seen to occur to the red car in the teaser does not match the more extensive damage to the car present when Mulder is examining it after the agents talk to the janitors.
When Willa signs and says "I love you, too" to Sophie, she actually signs "to" instead. The sign for "to" is different from "too." ASL doesn't have one sign for both words as the signs for each have different meanings.
Dr Ambrose when explaining about the difficulties to get elephants to breed in captivity says that only six such births have ever taken place. However in 1992 alone, there were 22 births to elephants held in captivity and in 1993 21 more. Records for elephant breeding go back to 1875, and shows a solid pattern of increasing successes.
When Mulder has the video call with The Lone Gunman, it's stated that they are communicating via satellite. Even by modern standards (2021), satellite communication is high latency creating a very noticeable delay between the time something is said, received by the other end, responded to and the time the response is received. In spite of this, they are able to immediately respond to each other as if they were in the room together.
Around 23:50, the tiger walks directly to a person that appears to be a animal trainer.
At 28m 24s the camera is pointed at Kyle Lang, sitting at his desk.
Willa Ambrose walks between the camera and Lang. This reveals that the camera is looking through a window, and some lighted shelving behind the camera is revealed in the reflection from the window. The next shot reveals part of the set, and the window behind which the camera was placed.
Mulder tells Willa Ambrose, "I don't know where they're being taken, but there's obviously some problem getting them back, due to what is probably an astrological variation, a trouble with the space-time continuum." The reference should have been to an *astronomical* variation.
In the prologue, when the "elephant" is on the rampage, the older janitor makes the sign of the cross as he is obviously quite religious. However, he crosses himself by going right to left. Catholics always cross from left to right, and anyone of Catholic upbringing would know this.