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Just as a point of clarification, most field surveys conducted with "plain table" were highly accurate. If the map you are using was created by the USGS or Coastal Survey (or their predecessors) the data will be of high quality. Your issue is selecting and using the best method for georeferencing your information. If you are georeferencing a topo map you should check to see if you have any benchmarks listed. You may be able to find their current coordinates and use them to georeference you map as well.
For step by step method for georeferencing historical maps take at look at http://proceedings.esri.com/library/userconf/proc98/PROCEED/TO300/PAP300/P300.HTM
Thanks having some of the same issues with the various old maps sites that everyone's suggesting or linking too. I'm finding that my RMS error is .03 yet SD / MT border is off as is South Dakota / Missouri when trying to GeoRef 1872 USA Atlas / 1874 MN atlas for a historical map display. I enjoy the challenge and maps available on David Rumsey or others maps just a projection or default suggestion would be appreciated.