Rust spots would come from a couple different things – could be bobby pins or other metal that drops to the bottom of the pool – could be nails – could be pennies if they were used to hold the liner in place at all?
More common is rust from well water.
They could also come from stainless steel screws or light housings, or the pool walls if the water chemistry is aggressive – which I have seen in even new pools – see the photo gallery for what this may look like.
Minimal Rust stains will come up with the addition of Natural Chemistry Stain Free and then treat to remove the iron from the pool – our FerriTabs work well for that. In the case of the severe issues from the water chemistry – treatment can be tried, more likely the liner and fittings should all be replaced.