I think the generally accepted definition of an omen is that of a sign or something that portends something in the future. As has been stated before, the modern idea is generally negative, although that needn’t always be the case.
In order for something to be a sign, I think it has to be unusual or strange. Just to give an example, where I live there are quite a lot of magpies, I’d spend all day counting them going to and fro, so it wouldn’t be much use to use the old magpie augury. On the other hand, if I were to see, say, a golden eagle, then that would be unusual, and that’s were (possibly) one could start talking of signs, in this instance augury. The ancients, in this case the Etruscans and Romans, had quite strict rules about when and how to read the signs, too – part of this being no doubt in order to avoid potential false cause fallacies or appeals to coincidence – seeing a frog in a pond full of frogs in spring is hardly much of a sign of anything.
As for the dimes, well, I’d say that finding dropped small change in a parking area is not really a sign of anything really, but lucky all the same.
Anyway, that’s my tuppence, or shall I say dime’s, worth! 😀