We just did that to the base molding in the 1965 house we bought. All the doors/trim/cabinets were custom made and matching.

Carefully removed base molding/door trim---pulling the nails out the back side to avoid splintering the face of the molding. Sanded it to remove the old finish and sand out some of the bigger dents/scratches/etc. Then restained with the original color---we have the advantage of knowing the original owner.

Finished it all with Sherwin Williams oil based varnish and reinstalled.

If the moldings are fairly pedestrian, painted, and/or extremely damaged, it's usually cost-effective to just replace it rather than stripping, sanding, staining and refinishing.

If you do decide to pull it off and re-apply, pull the nails out through the back to prevent damage on the front due to fillers and chipping.

You didn't say whether you wanted to preserve the 1969 look or if you wanted to update the look of the interior of the home. I don't know about you but me personally I would want to give new to the place with new molding/trim pieces. If you aren't sure purchase or ask for sample pieces that you can take home, put up and then decide what look is the one that best fits your design needs.