There were two problems with the staged nuclear strike. The first was the sound of the incoming missiles - ICBMs travel at supersonic speeds, meaning that they would reach their targets before the sound of their shock wave would arrive. The second was the flash and Collins' reaction to it. As a scientist working with weapons-grade fissionable material, he should have known that by the time the flash of a nuclear explosion reaches a viewer it is already too late to shield one's eyes.
Barney rigs Collins' radio with a tape player so that when he turns on the radio he will hear a report of a possible war breaking out. When Collins turns the dial he finds other, different, reports. This would be impossible without multiple tape players.
The IMF team places makeup on Collins' face to make him look older and he is not aware of it. Anyone who has ever worn facial prosthetics, such as he is wearing, knows that you are well aware that you are wearing them.