Other mistake: Down in the mine, you have to put night vision on Mulder to see what is going on. Yet, without night vision, Scully can still track and follow Mulder just fine.
Revealing mistake: At the start of the game, Mulder goes into a diner to look for a landline phone to make a call. Going into the back, the chef is chopping up something on the stove with a butcher knife, and at this point, he's supposed to be totally fine still. Yet, as he turns his head, and if you look from the back angle, you can already see his character model has half his face burnt and part of his body burnt and bloody from lying on the stove even before he turns and is found lying on the stove moments later.