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In truth, there's no real fail safe way to test this - but after a quick check over the risks are low enough that, in practice, I don't worry about it. I will however make a note of the following points:
Is the area that the lookout is on prone to erosion? This is perhaps the most worrying sign if it is, and is pretty easy to check just by how the cliff (or whatever else it is the rock is jutting out of) looks.
Examine the material - if it's wood, does it look well painted and maintained? This is easiest to tell with wood since if it's not it will generally look rotten and not something that you'd want to trust your life with. If it's rock, then are there any obvious cracks?
Does this look like a lookout post that's intended for use? Is it near a path where people would be expected to go, or is it a rough piece of rock that just happens to be there and looks like a look out post?
Do you even need to go on it? Sometimes I've seen particularly dodgy posts that I've avoided, but then on reflection realised that actually, the view is just as good from next to it, or a bit further down the path.