What should I realistically expect after having my floors professionally refinished?
All can be solved with money. Of course, at certain point it becomes cheaper to buy a brand new floor than keep fussing with an old one.

Nails become more visible after you sand a floor down. You can sink the nails by using a nail punch and then fill in the hole with a putty, but the putty has to matched to the color of the wood which is non-trivial. Sometimes nails will stain the wood, so you need to bore into the wood and make a larger filling. Also, you then need to redo the finish on top of this afterwards.

When a floor does not lie flat, usually that is because the joists below are not perfectly level. Sometimes this can be corrected by inserting shims between the joists and the floor boards if they are accessible (like in a basement), but it is tricky to do it. Ideally you make sure the joists are perfectly flat BEFORE you lay the floor down, and you use a subfloor.

In all honesty, the refinisher probably did all that was reasonable to do for the kind of money involved.