I thought about mentioning this in the OP, but WTF?! That stupid Prophecy wouldn't have gotten Voldemort shit. Knowing fantasy tropes like I do, there is of course some secret to the Prophecy that has yet to be revealed, but in the movie it just seems pretty cut and dry and boring.
I can explain the Prophecy. It's not a spoiler, because the movie could've explained it but didn't.
Flash backwards a few years, and Voldemort was standing on the edge of a brand new unexplored level of power. Probably enough power so that he wouldn't even have to worry about Dumbledore. Also, Professor Trelawney is a joke. She's almost totally useless. One of her ancestors was a powerful fortune teller, and she deluded herself into thinking that she was one too. Harry/Ron/Hermionie were right about her, but Harry and Ron enjoy the joke while Hermionie doesn't.
Now, Dumbledore was taking applicants for Trelawney's job, and during her interview she produced one of the only genuine Prophecies she's ever made. She said that a Chosen One was being born with the power to defeat Voldemort, and that they could not coexist peacefully, one of them would have to kill the other. Her description of this Chosen One perfectly fit
both Harry and Neville.
That's as far as Voldemort was able to hear, because his spy got cut off. But that was all he needed to know. The solution is obvious. Kill them both, immediately. He personally went to the Potters, and he sent Bellatrix to the Longbottoms.
But Harry lived and Voldemort died. Why? Voldemort came back from the dead and got killed by Harry's mother's protection spell. That must be it. Voldemort came back from the dead again, and beat Harry's mother's protection spell, but Harry still lived. Why? Voldemort needs to slow down and think this thing over before he proceeds and maybe kills himself a few more times. Dying repeatedly kind of hurts and is bad for his reputation. He needs to hear the full version of the Prophecy.
The last part of the Prophecy? The decision between Harry and Neville will be made by Voldemort himself. He will pick one of the two babies, and "mark him as his equal", and by doing so he will give that baby the very tools he needs to defeat him.
By attacking Harry, Voldemort gave Harry the scar, and gave Harry a copy of his powers. That's why Harry can speak Parseltongue. Without the scar and a copy of Voldemort's power, Harry would have probably been about as useless as Neville.
So there you go. That's the full version of the Prophecy. It's of no practical use to Voldemort whatsoever. All it did was troll him. If Voldemort had said "prophecies are stupid" and continued on his path to absolute power, he would have won the game, but because he was afraid the Prophecy might stop him, he flinched, and did exactly what the Prophecy said he was going to do.
And Dumbledore hid Professor Trelawney safely away in Hogwarts Castle and let students be taught by a delusional nutcase for more than a decade just to enhance the troll. Notice that when Umbridge tried to fire Trelawney for incompetence and kick her out, Dumbledore wouldn't let her be kicked out? Dumbledore didn't care about Trelawney the way McGonagall and the kids did, he just
really wanted to twist that knife in Voldemort's gut, at just the right time and place.