How to "call" a ball not caught?

[AtlUmpSteve]

As I understand it, the purpose of the "safe" signal when seeing a play where they think you should be calling something is to acknowledge that 1) yes, I saw it, too, 2) I have made a judgment, it is a "no call", and 3) coming out to argue with me is challenging judgment, so you better come out asking about the rule, or else suggesting a different angle might have additional information to add.

To me, the biggest positive is that it stops the "he wasn't looking" griping; you can disagree with my judgment, but you know I saw it, and ruled on it. Personally, I think it is a good thing, when used appropriately (and not over-used).