I think a lot depends on the sign itself, obviously, but also the observer’s situation, frame of mind, and, of course, personal/cultural factors; for example, in Britain a black cat crossing one’s path is generally considered lucky, but in many other parts of the world, this is considered to be unlucky. I was also once told that dropping things, such as cutlery, in the house was a sign that someone in the family was pregnant! The list could go on and on.
To my mind, it’s a bit like dream interpretation, it depends a great deal on the individual and the circumstances in which the “sign” was beheld. In terms of bird augury, the Romans had a very fixed set of practices and interpretations when it came to this kind of thing and unless it was something very, very unusual, I don’t think they would have just randomly interpreted birds flying around as a sign of anything, certainly not without any kind of ritual, creating of a sacred space, and so on beforehand.
I suppose you could think of it this way, a sign is something that draws attention, a notice of some kind, something that stands out, so my example of frogs in a pond would not constitute much of a sign.