Given Jeenodes are running at 3.3v and regular Arduinos at 5V I had the impression that the voltage could be anywhere in the range from 3.3v to 5v and from the thread I linked to, perhaps even a wider range than this.
With suitable changes to fuse settings, the Arduino can run at either 3.3V or 5V, not any random value in between.
Perhaps you're alluding to something bad which happens when the supply voltage changes while a sketch is running.
Yes, bad things happen when the voltage is not constant. Serial data transmission, among other things relies on clock speed, which is a function of voltage.
Perhaps you're trying to underline my ignorance.
Not really. Just questioning why you think that the 5V is not important.