IMO the more complex an object is the less able we can determine it has an artifical source. This is only becuase complex objects tend to be the least understood. And until something is understood to a reasonable level, it only makes sense that a natural explaination would be elusive. Of course once a complex object is fully understood we can determine the likelyhood of it having an artificial source in my opinion.
So with radio signals I reckon we are already in a position to determine whether a signal is artificial with high probability simply because we know so much about radio signals and sources. So there is little scope for finding a natural explaination for say detecting a radio signal containing the sequence of digits of PI.
As for the artifact on mars I think it depends on the artifact. Artifacts that we fully understand are actually easier to determine as artifical. For example the digits of PI carved into a rock face on mars would immediately imply artifical, as lots is known about geology, and carving, and nothing we know could come anywhere near explaining such a thing.
And that's what distinguishes this from your rainbow example, where lots was not known about atmospheric science and optics at that time. I think that if the main contention of the ID'ers was correct, namely, that the features and diversity of living organisms could not have come about through naturalistic processes, science would be capable of determining that, at least with a high degree of probability.