Does anyone have any thoughts as to how to fill and paint the holes left from removing emblems on a new 04 F250 SD without painting the whole panel?

 

as far as filling them remove the paint around the area how ever far you would have to to do this then weld the holes grind it down and repaint the area. unless you're trying to avoid painting altogether then I don't know

 

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The best (and only way I believe) is to fill the hole with metal. Hold a piece of copper (I use a flatten copper pipe) behind the hole and spot it with a mig, from the front side.

It is possible to spot paint the area. Your results will depend on the paint and the skill of the painter.