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One good example until it collapsed was the "Old Man of the Mountain" in Franconia State Park, NH. If the level of detail of the two were compared, don't you believe that the difference in detail alone would be sufficient to infer design?
Hmm -- I wonder if there is a natural process that produces faces in rock, the Old Man in the Mountain being where the process hadn't yet finished, and Mr. Rushmore being in more of a final state?
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Secondly, all four faces on the Mt. Rushmore carving are portraits of specific, documented historical figures.
But I know that those faces arose from natural means -- those four individuals grew from faceless embryos, and so the faces came about by way of the natural processes of developmental biology (based on the science of biochemistry) -- unless you want to hypothesize that a designer directly guides the development process.
So, we know that there is at least one naturalist process that can produce those very faces -- perhaps there are more that we are not yet familiar with?
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The marks themselves are too regular and from processes we are intimately familar with.
Ah! Now this is becoming compelling. So, if we assume that living species are designed, or that certain biochemical processes were designed, maybe there are tool marks to indicate this?
My point is that the analogy with Mt. Rushmore is a bad analogy for IDists to use. We already know
a priori that Mt. Rushmore was designed. If Mt. Rushmore is to used as an analogy, we have to pretend that we do not already know that it is designed -- and then try to figure out what characteristics it has that would lead a reasonable person to conclude that it was designed.
The tool marks is a good one -- my hat off to you, jar. I was thinking more on the lines that we know humans create sculpture, and know the processes humans use to do it, and so Mt. Rushmore looks all the world like things we know humans designed. But this is less compelling than your example, since it is possible that there are natural processes that can produce the same product. I like the tool marks.
I guess my real point is that the only method of inferring design that I know of is to compare the object under study with objects known to have been designed. I feel that your first two attempts fail since we know that the Old Man in the Mountain was not designed, and the real faces of the real historical figures also either were not designed or, at least, is still under contention.
This is where the IDist fail -- to show that some living system has been designed they need to find examples that are
known to have been designed and then isolate the unique characteristics of those designed systems to compare with the living systems directly.
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