Things I sorta don't get
The movie is not bad, but in the end I think it falls short. Predictable in places and weird in other places. If you don't want spoilers, then don't read any further. Anyway, here were a few things I did not get or thought were just odd:
1. They refer to this as reincarnation, but it's not really reincarnation. It is sort of like possession and reincarnation. And it's not clear to whom this happens. They suggest that it is people with unfinished business (e.g. the guy who came back to be with his mother), but who doesn't leave this earth with some serious unfinished business? (The scene with the bullet holes on the dude and then showing the blood on the baby was cool!)
2. Why did the killer get naked and commit suicide when he was caught? Did he have some reason to know that he'd come back in another body. Serial killers don't generally kill themselves. I mean why not give up and plan an escape, like Hannibal?
3. What happened to the babysitter (who fell down the stairs)? They almost suggest that she died, but something is odd there; it's as if they cut something out.
4. The part about the mom wanting to murder the serial killer's lone survivor is a bit odd. Most soccer moms don't become cold-blooded killers overnight, especially where the victim has had a hard life and has her own children. Not very credible, especially as there was no guarantee that this would work (which of course it did not).
5. The farmer shooting the mom is rather odd. Very strange he would come out there, with a rifle, and a shoot a strange woman; he wouldn't know if they were just playing a game and if it was a toy gun etc. And not even as much as a warning: "Hey, what's going on?" or "Can I help you?" No -- just shoot first and ask questions later. And not even just shoot her in the arm or leg; he was pretty darn close. (And this type of ending has been done before.)
6. The movie is called the "Prodigy," but the "prodigy" aspect of the plot is almost irrelevant to the rest of the movie. The movie still works if he's an idiot or a prodigy. So it's an odd name for the movie and an odd aspect to the movie.
7. The movie ends as if the kid will just continue with his mischief (e.g. eyeing that woman's hands), but his dad will likely recover (in an induced coma) and that other dude knows about the possession, and so at some point the jig will be up. Just some loose ends, unless you want to assume that the tot just wipes those guys out.
8. Speaking of the guy with all the expertise in reincarnation, they treat him as almost sort of a scientist, but there is no such real study nor a sufficient data set or way of researching this stuff. He says e.g. that the child must be fixed soon or else it's too late, but how the heck would he know? Is there a research study showing that the possessor leaves when the mission is accomplished, and that it's too late after age 10? That initial scene with him is also a bit awkward; you don't just dump the concept of possession-reincarnation on the family member of a possessed person in 2 minutes.
9. The kid seems to rebel when he learns that he's going to some sort of boarding school. But why would he care? If anything, he'll be away from the people who are savvy to his evil nature. Why not just go to boarding school, create mischief there, then get old and go commit more mischief? Who needs parents for that?
OK -- but again --- not a horrible movie. Pretty well acted, interesting ideas.