Since I wrench professionally and can build a wheel easy peasy I would probably just replace the rim and spokes, UNLESS the hub/cones were pitted. Going to a new wheel complete might introduce other factors like axle width/frame spacing or cog set fitting and compatibility. I wouldn't be too concerned about catastrophic failure or safety with using the old rim. Just the frustration of feeling the flat spot every revolution and as you use the brake. Loose spokes are the worse issue in the mean time.

So ride the bike and decide what to do ASAP. Andy.