Hi,
I'd vote to fill them. I agree about leaving the gaps, but the nail holes, looks like the job was not finished.
I watched the floor sanders do this once, and their technique was to hold a well kneaded ball of putty between thumb and forefingers, roll it a bit to a point, press it hard down into the hole, and slide a sharp spatula along the floor under this with the other hand. No need to finish off at all.
Cheers