I've thought about this and my conclusion is that we will likely leave behind a very strange pattern of certain natural resources. "Oh, look, here's a vein of copper! It's getting better, and better, and, that's weird, it's gone now and there's a complete break in the strata for some reason." Over time new mountains may form some new deposits, but it may be noticeable in the older mountains (that are today the younger mountains) for a long time.

If we make it for another few hundred years, not only will there be a mass extinction, but there will also probably be a traceable sudden explosion in a novel form of gene transfer and creation that can't be explained by any other theory. The modern fashionable self-loathing idea that we are a uniquely biodiversity-destroying organism may be merely a consequence of our current point of view; rather than "extinction" this could in fact be an inexplicable explosion in diversity if you could see 1000 years into the future. But of course the mass extinction will still be there. I haven't done an analysis but it may also be the case that the extinction has a very characteristic pattern; again, rather than the fashionable self-loathing model of "humans just destroy everything" it may be noticeable that fauna died out in favor of things that are clearly domesticated even just from their skeletons, and that human predators were preferentially extincted, etc.