I would be very leery of any attempt to "putty" the screw heads at this time. I assume the screw heads are sanded into, and showing bright metal. Where does the putty go in that case? In my opinion, the only way to fix this is to back out each screw, deepen the screw pocket, install new screws, and plug. This will require careful sanding of each plug to level it so that a large area around each hole is not sanded through to bare wood. Poly the sanded plugs and let dry. When finished, lightly scuff the entire poly floor, and recoat. This is labor intensive, and will not be a cheap fix.

When my daughter's floor was sanded, I asked the flooring contractor about nail holes and exposed nails. His answer was that he was a floor finisher, not a carpenter. I did the repairs myself before he sanded.

If you are down to the screws fastening the wood with sanding, you should replace the floor. At this point, the best outcome you can have is to have some of the money refunded so you can replace the old floor and have another contractor finish it. Wood putty isn't an acceptable fix when you are down to the fasteners. You can't put enough putty onto a screw surface exposed by sanding to adhere at all remotely long term.

Yes, this guy was sleazy and should have told you this from the beginning so that you didn't waste time and effort on this floor. He is also probably technically correct about doing the job you hired him to do. He treated you like a GC who knew what he wanted and was contracting specifically for that job only with no additions and subtractions. Somewhere on this job there is a big lack of communication. He presumed you to have the knowledge to be able to specify the job when he should have treated you like a unknowledgable homeowner and educated you about the work to make sure you understood about the options you had. Take this as an educational experience and learn to ask more questions about the process before hiring a tradesman.

Also, the written word rules, so any contract that you enter into with a tradesman needs to spell out the job exactly and leave no assumptions floating around. Those will bite you. If your written contract only specifies sanding and coating the floor, then that's exactly what you got, whether or not the floor is in good shape and usable after that sanding or not. What exactly DOES your contract say?

Srjohnt.... This contractor will not do this work. The best I will get from him is one more coat of poly. I am going to fill them myself...the ones that can be filled. It is not going to be a perfect floor. I am disappointed... I think it has become a choice between living with the major imperfection and replacing the floor. So, at this point, it is a question of to putty or not. I am going to try, because I could see that they were going to touch a couple up and get out of here.
I see a beautiful carpet mid floor! I have had to learn to deal with disappointments and let me tell you it is a valuable lesson.

Live wire... You are so correct. I told him as much... he did exactly what he said he would do. Imagine though, if someone were hired to replace a roof for example and found rotted wood underneath... just to put the new roof on as contracted would be irresponsible. We had no reason to ask about replacing the floor. However, we were satisfied with the floor as it was previously and did not anticipate that screw heads would be a problem. I think that someone who does this for a living should have been able to anticipate this problem. If not prior to sanding, then at least his workers should have been able to point it out after sanding....or he should have inspected prior to placing finishing coat on. We could have re-evaluated the job at that point if necessary. I think too many workers just do what they can to get their money and do not think or have pride in their work.
Unfortunately for him, if and when we do replace the floor, he will not get the job. For now, I am going to try to make it look the best that I can. Tonight, my DH and I will discuss replacing the floor, but considering that we do plan to sell, and our home is probably already over-invested in for some of the neighboring homes with this square footage, I imagine that it will not make a difference in the ability of our home to sell and would be a financial loss to us to do so.