Is it safe to place a capacitor across vin and gnd?
I have a 3A fan hooked up to an ATX power supply in parallel with a transformer which powers my board through VIN/GND.


I don't entirely follow that wording. Please draw a picture.


  I have place a 470μF capacitor accross the Arduinos VIN and GND pins and it seems to have stopped the problem, but I'm not too experienced using capacitors. Is this an apropriate value? I'm not sure what difference it would make. And is this a wise move as I so think?


470µF is fine. In this situation the bigger the better. If 470µF fixes it then 470µF is fine. Don't be afraid of going higher though. I have 3,300µF capacitors here that are commonly used for similar purposes.

What you have implemented is called a reservoir capacitor and is a common use for large value capacitors like that.