I think the wave function of a free electron is nonzero almost everywhere. In particular there are regions of space arbitrarily far away where the electron has positive probability of being found. If I prepare an electron in a particular position, then wait a small amount of time and then check to see if it has appeared in a region that is too far away for it to reach even if it traveled at the speed of light, there is a positive probability that I (or my assistant, who is coordinating with me) will find it there.
What have I missed? This seems a lot like spooky action at a distance, but with spooky action no matter/information actually moves faster than light, wheras in this situation the electron actually moves a greater distance than light could in a given amount of time.