JK mentioned the importance of 'Why did Albus Dumbledore have James Potter's cloak?'
Feel free to help me and correct me where I'm wrong. :)
1. Why would James want to hide the cloak?
Would people come to Godric's Hollow to look for it? Is it an important artefact, like a possible Horcrux? (Then why didn't Albus destroy it instead of giving it to Harry?) Is it stolen? Who would be looking for it?
If James wanted to hide it he could have put it in his vault at Gringotts. He gave it to Albus instead, perhaps because someone needed it? Not Albus himself, he can be invisible if he wants to. But someone else might need it. At this point the war is high and Alastor Moody, who owns two cloaks (at least in 1995 he does, perhaps not in 1981) might be using them.
Who was where at Hallowe'en's night?
James, Lily and Harry were with Voldemort at Godric's Hollow. That's all I truly know.
So where was Albus Dumbledore?
At Hogwarts? Did he help to make Peter the secret keeper instead of Black? Then maybe Albus wanted Black to escape into hiding using James' cloak. But while Black and Albus were looking for a way to make the bluff work Peter went to Voldemort and sold out the Potters. Then when didn't Black and Albus realise Peter was the spy and the Potters were dead (except Harry ;) you knew that.) Why did they trust Peter and didn't check on the Potters when they knew there was a 'rat' in the order?
Where was Severus Snape?
If he'd been at Voldemort's place he'd have known Peter was the spy. Voldemort probably doesn't trust anybody but himself so he wouldnt have told Snape about Peter. Snape didn't know and wasn't there. Was he at Hogwarts? Then why didn't Black know Snape was working for the order? It's possible Albus didn't inform the order about Snape's work, possibly because of the leak in the order. Then why did Albus trust Snape? Could Snape have been at Godric's Hollow to keep an eye on the Potters? He knew about the prophecy and was working for both sides, he could have gotten away with it as a DE and as member of the order. Then why didn't he help Lily and Harry to escape while Voldemort and James were in a fight? Did he flee? Did he use James' cloak to guard the Potters and did he give it to Albus afterwards? Is that why he knew/suspected Harry had the cloak and why he hates Harry so much, because he failed that night?
Where was Peter?
Probably at Voldmeort's place waiting for his master, when he realises something went wrong he'll have fled and run into Black the next day.
My guess is Albus got the cloak back from Snape and kept it until he could give it to Harry as a gift. Quite a wild guess. :)
ETA If this were true it would also mean Snape thought Black was the double crosser, which will not have helped when he finally meets Black in the Shrieking Shack.
ETA 2 The official Harry Potter site
here has a rumours section where JK Rowling says Snape wasn't hiding under the invisibility cloak at the night the Potters died. Which means I'll have sleepless nights to find an answer why Albus had the cloak.
:) Yay for plot theories between the books, we're lucky to be waiting for book Seven.