I came across an old essay on the Harry Potter Lexicon dated 17th January 2001, written after the release of Goblet of Fire when many details about Voldemort's attack at Godric's Hollow were still unknown. Intriguingly, it floats the idea, on the basis of what is written in the first four books, that Voldemort couldn't have attacked both Harry and Lily/James.

According to JKR (Diane Rehm show, 10/20/99), "Voldemort killed James and Lily, then tried to kill Harry." This is clearly what she intends. It is not, however, what it actually says in the books. This page discusses what the actual text states and what that would mean. Clearly, JKR doesn't intend this to be the way the story goes. But this IS the way it's written. 

Everything that was known for sure about the events at Godric's Hollow in 2001 was based on the voices Harry hears when in the presence of a Dementor, Voldemort's own first-hand testimony of that night after he returns and the Priori Incantatem in the graveyard. Yet the Priori Incantatem contains a key omission - the Avada Kedavra cast at Harry by Voldemort (one of the most important events in the whole story!).

The article's summary of the Priori Incantatem is as follows:

• Cruciatus Curse cast on Harry by Voldemort a few moments before (comes out as screams), June 24, 1995




• conjuring of a magical hand to replace the one Wormtail cut off, cast by Voldemort after regaining his full body, June 24, 1995




• Cruciatus Curse cast by Voldemort on Avery, June 24, 1995




• the murder of Cedric Diggory with the Killing Curse, cast by Wormtail on Voldemort's command, June 24, 1995




• Cruciatus Curse cast on Wormtail, witnessed by Harry in his dream, cast by Voldemort, exact date unknown, but somewhere around the last week of May, 1995




• the murder of Frank Bryce with the Killing Curse on the evening of August 20, 1994, cast by Voldemort in his "ugly baby" form, from his chair in the Riddle House




• the murder of Bertha Jorkins, exact spell inknown, cast by Voldemort, summer of 1994, some time before August 20




• the murder of James Potter, exact spell unknown, apparently cast by someone other than Voldemort and probably NOT at his direct command, on the evening of or sometime after October 31, 1981.




• the murder of Lily Potter, exact spell unknown, also apparently cast by someone other than Voldemort and probably not at his direct command, also on the evening of or sometime after October 31, 1981.

Since the attack on Harry isn't mentioned the writer logically concludes that the murders of Lily and James took place after the attack on Harry in which Voldemort lost his body, and that therefore Voldemort must have had an accomplice when he went to Godric's Hollow.

The evidence that we do have from the Priori Incantatem suggests that James and Lily were killed using Voldemort's wand AFTER Voldemort attacked Harry. After all, the last nine spells that wand cast included the ones that killed the Potters but DID NOT INCLUDE THE ONE THAT ATTACKED HARRY AND REBOUNDED ONTO VOLDEMORT. This mystery still remains, no matter in which order Lily and James came out of the wand. Who, if Voldemort was unable to cast a spell, killed James and Lily Potter?

We know from the later books, most notably from the description of the attack in Deathly Hallows, that this wasn't what really happened. Yet the Priori Incantatem gives that impression. To fit with the order of events in the other books the Priori Incantatem should have gone:

• The murder of Bertha Jorkins.




• The failed attack on Harry Potter using Avada Kedavra.




• The murder of Lily Potter.




• The murder of James Potter.

Yet it didn't.

There's no mention of the Avada Kedavra in the text, which moves straight from Bertha to Lily.

But already, yet another head was emerging...and this head, grey as a smoky statue, was a woman's...Harry, both arms shaking now, as he fought to keep his wand still, saw her drop to the ground and straighten up like the others, staring...

The shadow of Bertha Jorkins surveyed the battle before her with wide eyes.

"Don't let go, now!" she cried, and her voice echoed like Cedric's, as though from very far away. "Don't let him get you, Harry - don't let go!"

She and the other two shadowy figures began to pace around the inner walls of the golden web, while the Death Eaters flitted around the outside of it...and Voldemort's dead victims whispered as they circled the duellers, whispered words of encouragement to Harry, and hissed words Harry couldn't hear to Voldemort.

And now another head was emerging from the tip of Voldemort's wand...and Harry knew when he saw it who it would be...he knows as though he had expected it from the moment when Cedic had appeared from the wand...knew, because the woman appearing was the one he'd thought of more than any other tonight...
_{(Goblet of Fire, Chapter 34, Priori Incantatem).}

No description of the Avada Kedavra there. And yet we know that Priori Incanatem reveals all spells, not just murder victims. Hence it produces screams to represent the Cruciatus Curse and recreates Wormtail's hand and the Dark Mark in ghost form. So the Avada Kedavra should have appeared but didn't.

Is this just an editorial oversight or is there an in-universe explanation?

We simply do not know enough about how Priori Incantatem works.

Consider the following:

It does not appear to show all spells – as I noted in a comment, Voldemort cast at least four other spells in the graveyard that did not appear.

• A spell forcing Harry to bow


• The Imperius curse on Harry


• An unnamed curse that hit Voldemort's father's headstone


• The Killing Curse that collided with Harry's spell

Moreover, there is conflicting evidence as to what the wand should show. When Dumbledore explains it he says:

One of the wands will force the other to regurgitate spells it has
performed – in reverse.

The only thing that came out of Voldemort's wand that could be termed a "regurtitation of his spells" was Wormtails hand. Voldemort had conjured a silver hand so the wand showed a silver hand i.e. it is as if the wand is recreating the spell. However, when it comes to the Cruciatus Curse and the Killing Curse, the wand displays screams and the victims which are not recreations of the spell but the effects of the spell and the people it was cast upon respectively.

If we look back to the beginning of Goblet of Fire, we find another instance of a wand showing its recent spells:

"Well, we'll soon see," growled Mr. Diggory, looking unimpressed.
"There's a simple way of discovering the last spell a wand performed,
elf, did you know that?"

Winky trembled and shook her head frantically, her ears flapping, as
Mr. Diggory raised his own wand again and placed it tip to tip with
Harry's.

"Prior Incantato!" roared Mr. Diggory.

Harry heard Hermione gasp, horrified, as a gigantic serpent-tongued
skull erupted from the point where the two wands met, but it was a
mere shadow of the green skull high above them; it looked as though it
were made of thick gray smoke: the ghost of a spell.

Here, Harry's wand recreates the spell, as Voldemort's wand did with the silver hand, and as Dumbledore described it. Moreover, it is clear from Mr. Diggory's words that this must be how it works – if the wand would merely show the victims we would not actually know what spell had been cast.

Additionally, there is another example of Priori Incantatem mentioned in Deathly Hallows when Harry explains how Voldemort would know that Harry's wand was broken:

"Priori Incantatem," said Harry. "We left your wand and the blackthorn
wand at the Malfoys', Hermione. If the examine them properly, make
them re-create the spells they've cast lately, they'll see that yours
broke mine, they'll see that you tried and failed to mend it, and
they'll realize that I've been using the blackthorn one ever since."

Harry refers to it as "re-creating the spells", yet it is clear that it would have to show the results. If it only showed the spells they would have no way of knowing what was destroyed and what was attemptedly mended.

Thus, there is just too much conflicting evidence about Priory Incantatem.

It may be because the curse rebounded and didn’t kill anyone.

The Killing Curse that the Dark Lord cast didn’t actually kill anyone. It didn’t kill Harry because it rebounded, and the Dark Lord’s soul was ripped from his body but because his Horcruxes tethered him to life he didn’t die. Since neither of them were dead, there might not have been anything for the Priori Incantatem to show. It didn’t do anything like what he’d wanted it to do.

“He pointed the wand very carefully into the boy’s face: he wanted to see it happen, the destruction of this one, inexplicable danger. The child began to cry: it had seen that he was not James. He did not like it crying, he had never been able to stomach the small ones’ whining in the orphanage –

‘Avada Kedavra!’

And then he broke: he was nothing, nothing but pain and terror, and he must hide himself, not here in the rubble of the ruined house, where the child was trapped and screaming, but far away … far away …”
_{^{- Harry Potter and the Deathly Hallows, Chapter 17 (Bathilda’s Secret)}}

All the other spells we see shadows of in the Priori Incantatem (like Wormtail’s hand, the Cruciatus Curses (if that’s indeed what the screaming was) and the killing of everyone who appeared) are successfully cast spells that did what the Dark Lord (and presumably the wand itself) intended. It’s unclear what would happen in the Priori Incantatem for a failed spell, that rebounded on the caster and didn’t work as intended. The only effect it did have is to rip the Dark Lord from his body, and as that’s in no way what he intended, it might not have “counted” as his previously cast spell. He never cast a ‘rip me out of my body’ spell - he cast a spell to kill Harry which didn’t work. The wand might not ‘think’ it cast anything there, since the intended Avada Kedavra on Harry failed and no one died.

Another theory - there may be other factors in what’s “reflected”.

Something else to consider - the Priori Incantatem may not be reflective of every spell that the Dark Lord had cast since the Potters’ deaths. He’d turned Nagini into a Horcrux after that, and had used a few spells of his own invention to strengthen himself and create his rudimentary body, but none of those are shown.

“However, he was the able-bodied servant I needed, and, poor wizard though he is, Wormtail was able to follow the instructions I gave him, which would return me to a rudimentary, weak body of my own, a body I would be able to inhabit while awaiting the essential ingredients for true rebirth … a spell or two of my own invention … a little help from my dear Nagini’ – Voldemort’s red eyes fell upon the continually circling snake – ‘a potion concocted from unicorn blood, and the snake venom Nagini provided … I was soon returned to an almost human form, and strong enough to travel.”
_{^{- Harry Potter and the Goblet of Fire, Chapter 33 (The Death Eaters)}}

He explicitly stated he’d used spells for creating his rudimentary body, it would have of course been after the Potters’ deaths, but no spell like that is seen in the Priori Incantatem. Why these spells aren’t shown isn’t clear, but they aren’t despite being in the correct time frame. Those had been successful as well but still weren’t seen. It’s also possible that the attempted Avada Kedavra may be not seen because of whatever governing factors made the rudimentary body spells not be shown either.