Revealing mistake: In the end when Mulder is reading the paper in the park. The paper is clearly a prop. Only the frontpage is real - when he puts the paper away you can see that the rest of the paper consists of blank pages. (01:45:45)
Revealing mistake: When the booby-trapped car explodes, the detonating wire is visible running out of the exploding car and out of shot. (01:22:55)
Revealing mistake: Near the beginning as the helicopter arrives to take the boy away, a man steps on a tumbleweed. The weed bends as he steps on it, and it is flat. It is a prop.
Answer: Mulder has just hit rock bottom and is questioning just about everything at this point, so drinking is not really out of character.
Grumpy Scot