Off the top of my head it seems like Mirkwood Blocks, and therefore Mirkwood Offerings are finite resources - when all the old logs and stumps are gone, that's it for those curios.
Acre clay seems similarly finite, or does it regen and fill in these deep divots I see in clay fields?
Ore, but not stone, because stones can be had for free from mountain biomes.
Obviously the world is huge and I'm sure the existing resource will outlast the game, probably won't ever hit Peak Mirkwood, but I'm wondering what other resources out there cannot be replaced?