Skinner claims that because of some sort of advanced copy protection, the DAT tape was impossible to copy, or even print a hard-copy from. Yet in the opening episode of this arc ("Anasazi" from season 2), we see Scully providing a hard-copy to a Navaho woman for translation (and how did Albert translate the information in the first place? Surely, even if he had to read it off a computer screen, he would have created a translation that could be copied).
When Skinner and the Smoking Man meet in the former's office after Skinner has been beaten up in the hospital stairwell, there are no signs of the damage to his face from the attack.
The old Indian, Albert, goes to the hospital and meets with Scully's mother. He has no facial injury from the S3E1 where he had the butt of a rifle smash his cheek, which left a very large gash.
When Mulder finds his sister's file, the long shot shows the name is somewhat faded. The close-up of the name however, is very darkly typed.
Scully and Mulder use Napier's Constant (also known as Euler's Number) to gain access to locked doors using an electronic keypad at an abandoned mine. Mulder checks with Scully that Napier's Constant is in fact "27828" and she confirms that it is. However, the constant is NOT 27828, it is actually 271828 (or 2.71828...). Without the number "1" in the sequence, Scully and Mulder should not have been able to enter any of the doors.
Scully mentions that DNA was not discovered until 1944. The molecule was originally found in around 1860 by a Swiss chemist called Johann Friedrich Miescher. Watson and Crick deciphered the structure of the double helix in 1953
(at around 16 mins) Mulder and Scully enter the old abandoned mine as they walk through the door of the mine for the first time part of the wall is missing and outside you can see 4 people and a pitbull sitting on a ledge and ground taking a break and watching the shoot.
46th Street in New York City is depicted with a picture of a building on a two-way street. 46th Street in New York City is a one way street.
Mulder and Scully enter the vault punching in Napier's constant or a version of it on electronic keypads. If this was an operation in the 1970s, the key pads would not look as such. However, they could have been updated by the Sydicate over the years.