Chapter 3 of Half-Blood Prince makes it very clear that Grimmauld Place has more protections placed on it by The Order than just the Fidelius Charm:
We do not know whether the enchantments we ourselves have placed upon it, for example, making it Unplottable, will hold now that ownership has passed from Sirius’s hands.
My question is this: What's the point of these additional protections? The impression that I got from the earlier books in the series, particularly Prisoner of Azkaban, is that the Fidelius Charm's protection is flawless unless the secret-keeper leaks the secret or you're an owl (something that even the additional enchantments didn't block). Given that Dumbledore is said secret-keeper, the chance of him exposing the secret is small enough to ignore, so what other reasons were there?