Dumbledore, Pettigrew and the Spy (Was: Snape didn't murder the Potters)

[rbookworm46]

No: HPFGUIDX 138601

Del:
Even DD could probably be dragged in this mess, as the Head of the 
Order of the Phoenix (one could wonder how Peter managed to hide his 
treason from one of the two greatest Legilimenses in the world for 
so long).

Bookworm:
This question has occurred to me, too.  During CoS, he calls Harry 
into his office simply to ask if there is anything Harry wants to 
tell him.  Of course, everything Harry doesn't want to say enters 
his mind before he tells Dumbledore there is nothing.  Later we 
learn that Dumbledore, as a Legilimens, really could "see"
it.  

1. Did Dumbledore not use Legilimens to find the spy?
2. Was Pettigrew an accomplished enough Occlumens for Dumbledore not 
to detect him? 
3. Did Dumbledore know and use Pettigrew to pass misinformation? 
4. Any other possibilities?

Ravenclaw Bookworm