What should I do about my landlord suing me for property damage that was there when I moved into the rental?
Legally, you are not responsible for damage you, your family, your pets, or your guests did not cause. That would certainly apply to damage which predated your tenancy.
Practically, the issue will be whether the landlord can prove that you did do the damage; since he is suing you, the burden of proof is on him. That means he has to provide evidence that makes it more likely than not that you did the damage. If he can prove that in a court of law, then he could win. You should marshall any evidence you have (photos, notes or correspondence, anyone who can testify on your behalf) that you did *not* do the damage. Depending on the amount, since even defending a lawsuit can get expensive, you may wish to consider settling--even if it's unfair to pay something when you're not at fault, it may end up being the cheaper option.