The strangest thing is that in the dream you don't really notice. It's really quite odd - there's Jack and of course there's Jack as well.
Often one of them is a lesser instantiation - they have less talent or inspire less fear. You say I thought Jack was frightening but they're nothing compared to Jack! Sometimes it's something less negative - Jill will show you something and you think That's interesting - I bet Jill would like that, I'll have to remember to tell her about it!
This last one sometimes occurs in real life - when Jill shows you something just for a second you think that Jill would be interested and resolve to tell her before remembering that the notion is ridiculous.
It must be caused by an error in brain processing. A person is probably represented in the memory space by a complex object with myriad properties and associations. Perhaps sometimes two versions of the object are called into being by accident. Whilst awake the error trapping is probably far more stringent which is why the impression is momentary but when dreaming it's another matter altogether.
In dreams it's the pattern recognition part of the brain, the infamous Question Machine, that drives what you imagine is happening to you rather than any external stimulus so it's quite possible for you to "recognise" (which in a dream simply means "conjure up") two different person objects as having the same identity. Most of the time you probably don't spot the anomaly but sometimes it comes to your attention.
Continuity errors in dreams can be disturbing if you notice them. Sometimes a dream will throw up a non fact like "that time you spent in Australia last year" but not have any false memories to back them up with. The practical upshot of this is that if you notice this anomaly you begin to worry in the dream that you are losing your mind or your memory. This often happens to me - dreams spent in a semi panic due to the fact that I don't really recall something major that I know has happened to me (in the dream world).
Spotting mistakes in dreams can also happen when there are accidentally two versions of a person. However, because the person doubling is so much more "real" than the lack of memories about a supposed past event (sometimes both versions of the person are in your field of view at the same time) there has to be a semi rational explanation. Thankfully there are many possible explanations for double people - the second version could be a clone or a sibling (both of which explanations I've seen used in one recent dream which actually contained two sets of double people).
But why does this happen in the first place? Well due to the way that dreams may work it could well be that the people who end up doubled are ones who are very much on your mind. When attempting to make sense out of the red noise of unconsciousness the expert pattern recognising question machine that is your subconscious picks patterns that you've been thinking about a lot. As a result our dreams are usually populated with our hopes and fears, sometime those that we didn't even know we had.
Next time you dream of two versions of the same person ask yourself whether you should be paying them more or less attention in real life. If there was a noticeable difference between the two this may give you further clues.
Dreams may not predict the future but they can certainly shape it.