I own a condo in Seattle that I rent out. (Side note, I'm selling it because the hassle of owning it isn't worth the meager profit it provides.) Here's what I understand about the situation.

You are absolutely responsible for costs incurred bringing it back to livable standards so that it can be rented out again. This includes cleaning, painting, replacement/repair costs for carpets, curtains, appliances, etc. You can be liable for the actual amount of damage caused even if it's greater than your deposit. It's also completely legit to hire a professional crew to perform needed cleaning/repairs. You should also be aware that damage isn't always obvious to tenants. If you smoked in the apartment, for instance, it might need professional cleaning and repainting even though it looked fine to you. Or if you had a pet he needs to remove all potential allergens with a more intense cleaning than usual.

However he can only charge you for damage that you caused beyond normal wear and tear. The landlord can't use you to bankroll replacing old carpets or upgrading his property unless you specifically caused the damage.

Bottom line: The claims as he's stated are probably legit as long as his characterization of the damage is accurate. So disputing the extent of the damage is really the only way you'll get any relief. You both should have taken extensive photos for documentation. Rather than debating the semantics of 'damage' and 'wear-and-tear' ask to see his photographs of the damage he's charging you for along with invoices documenting the costs to repair it. If he doesn't have documentation, show him your photos and ask him to point out the damage.

My advice: If you disagree with his assessment of the damage or he refuses to provide valid documentation tell him that you won't pay. If he actually follows through with a collections attempt (unlikely unless you're not being honest about the state of the apartment) with such shoddy evidence then sue him in small-claims court. Make sure to seek legal costs as well.

If you didn't take any photos and he does have more solid evidence, then this may torn out to be an expensive lesson in documenting your rentals when you move out.