The tasks that lay before this group were 1) to survey and mark the 40 mile border of the District of Columbia (a 10 x 10 mile oblique square), 2) to survey and map the area for the city of Washington, 3) to produce a plan for the new Capital City, then 4) to mark that plan 'on the ground'. This process hasn't changed much since that time, except for the sophistication of the instruments that are used.
Remember that, contrary to what Nicholas Mann says, the planning maps that were being produced were intended to show where things were 'really' going to go, since lots were to be sold to finance the building of the new city. Mann recommends that the maps that we see were intended for the President's approval only, and were not the 'real deal', so to speak. He suggest a possible error of 20 yards in a mile. A 1 degree error puts you off 90 feet at one mile. [Tan 1 degree = .017, and .017 x 5280 ft = 89.76 ft.]
Serious students will want to read Bob Arnebeck's book "Through a Fiery Trial", about the history of the city. In that you read where auctions of lots were held, and the reason that L'Enfant was fired was because they had no finished map at the time of the first auction. The maps were not approximations awaiting the President's approval, but were accurate depictions of lot corners, etc.
In modern times, after the area has been surveyed and mapped, the plan has been approved and laid out on the ground, and the streets and utilities have been positioned, an 'as built' survey is done, to show where things really got placed. This survey is compared to the plan to check for 'fit'. As you can imagine, surveyors work closely with lawyers as well as realtors.
I will point out that authors like Nicholas Mann, Jim Alison and David Ovason never worked with surveyors, so their ideas about how the city was laid out are not from a surveying perspective. In what follows, I will apply a surveyor's eye to problems that surround the planning and construction of Washington, D.C. This will include critiques of ideas presented by Mann, Alison and Ovason, from a surveyor's point of view.
At one point, Mann suggest that surveying circles with a diameter of a mile or two would be like marking a circle in the sand with a stake at the center using a rope. Even a non-surveyor should be able to see the problem that arises from trying to use a rope a half or a mile long; that is just silly. As I say, he never surveyed and probably never talked to a surveyor about the map.