To make the nail hole disappear, be sure to use a countersink tool to recess the nail head. Some plastic wood filler, or other types of compounds, contain resins and other chemicals which can create marks in your wood. By staining the wood or applying the urethane first, then filling the hole, you will avoid the discoloration.

Wood putty comes in different colors and you can mix them to get the correct color match. Fill the hole only part way to check the color match.

Once the hole is filled, put one additional layer of stain on the entire piece and you won't be able to see where the holes were.