Geodesy, Coordinate Systems, and Positional Accuracy
Datums and surfaces
A horizontal datum is realized by a reference frame tied to an ellipsoid; a vertical datum relates to the geoid through orthometric heights. Know the difference between ellipsoidal and orthometric heights and know that coordinates are only meaningful with their datum, realization, and epoch. Mixing NAD27 and NAD83 values, or coordinates from different epochs, produces errors that look like blunders.
Projections and factors
Map projections are conformal, preserving angles but not distances. State plane and UTM coordinates are grid values; ground distances must be reduced to the grid and grid distances expanded to the ground. The combined factor is approximately the scale factor times the elevation factor. Convergence is the angle between grid north and true north and must be applied when converting azimuths.
Accuracy
Report positional accuracy as a statistic, distinguishing network accuracy from local accuracy, and do not claim more than the control supports. GNSS-derived positions are only as good as the control and the processing; published passive control should be checked before use.
Traps in questions
Applying the combined factor in the wrong direction; ignoring convergence; using grid distances as ground distances at high elevation; treating an OPUS solution as an unassailable coordinate; forgetting the datum in a legal description.
Rule of thumb
Ground distance equals grid distance divided by the combined factor, and combined factor is approximately scale factor times elevation factor. Record the datum, epoch, and units with every coordinate you publish.