Blaise said:
1. Dumbledore is the only one Voldemort feared.
2. Dumbledore is/was the most powerful wizard of his time
3. Dumbledore knows magic and places that would have kept him uncompromised
4. The Potter were in an order headed by him - they also seemed to share a more close relationship with Dumbledore than most
The thing is also, most of these points can be proven through looking closer at the books thus far.
1. We are told straight out that Voldemort feared Dumbledore, in fact, as I am sure you all know, there is a chapter titled after the fact.
2. We have had many characters say that Dumbledore is the most powerful wizard of their time, that is really all we have to go on....
3. I think this one is also best proven in OotP as well. After the scuffle at Hogwarts, Dumbledore should have been captured, but he wasn't, and the reason for that is that he knows where to go and what to do to protect himself, and he would have been able to do the same for Lily and James.
4. Everyone in the Order, with the exception of Snape, is like a family. Members of the Order helped the kids make the HQ fit to live in and have meetings at, they also often came for dinner when there were no meetings.
I think they were all very close, and as such, they should have chosen the best possible candidate, that being Dumbledore, to be their secret keeper. What we need to figure out is why. Did they have a reason not to trust him?