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.
Chosen answer: If they had put an "Out of Order" sign, or left it unilluminated, someone in charge might try to have it fixed or replaced, or could have checked to see if it's plugged in, etc. By leaving it illuminated, it doesn't look out of place and simply not taking money wouldn't arouse too much suspicion. In my own life, when I've come across a seemingly working vending machine that won't take my money or dispense drinks (but gives my money back), I just find another one instead of calling someone or reporting it. But yes, it is very convenient to the plot that Mulder just happens to try and use this particular machine.