Consider the classic example to show that simultaneity does not hold:
Have a photon gun firing two counter-propogating photons from the center of a moving train. The observer inside the train sees both photons hit the ends of the train simultaneously, whereas an outside observer sees the photon hit the rear-end of the train first.
Now if you modify the experiment by adding two photosensitive devices on the end of the train, and have an explosion that occurs when both photosensitive devices are triggered simultaneously.
From the reference frame inside the train, since the photons hit both ends simultaneously, the explosion will occur and the train will blow up.
However, from the reference frame outside, since the events are not simultaneous, nothing happens.
Clearly you cannot have two possible outcomes to the same event, but how do you resolve this apparent paradox?