Many purportedly-straight-line east-west state boundaries were first surveyed in the period from the 1600s up until the early 19th century, such as the northern and southern boundaries of Massachusetts, the Mason-Dixon Line, the southern boundary of Virginia, and the northern and southern boundaries of Tennessee.
Many of these boundaries notoriously deviate from being straight lines. Given that surveying lines of latitude (as opposed to longitude) was a well-understood technology during that time period, and land surveying lacks many of the challenges of naval latitude reckoning, why were there so many surveying errors, and why are some of those errors so severe?
Short answer:
"land surveying lacks many of the challenges of naval latitude reckoning"
And has other, often more difficult challenges. North American longitudes had technical problems; latitudes were simpler but still faced the difficulty of finding the specified parallel in the terrain.
Discussion:
Take a look at the terrain. Surveying in frontier America was often some combination of bushwhacking and mountaineering, access to places described by latitude and longitude were often physically impossible. And hauling delicate equipment and maintaining it in such circumstances wasn't easy.
As an example, here's a description of some of the problems faced with the Willamette Meridian:
On July 9, James Freeman gazed over rock ridges, some as high as 4000 feet. "On crossing [Calapooia River] at this point the line would extend into the Cascade Mountains through which it appears impracticable to extend the Meridian Line." The situation warranted making an offset, a line measured at right angles to avoid the impassable terrain p.59
The Bureau of Land Management "Field Notes" are the records made by the survey parties, and they're filled with tales of misery. Clambering through ravines and over mountains, animal attacks, disease, snow and floods . . . this was difficult work. Surveys in the Northwest are often carried out with these "offsets", a process which can readily lead to error.
Arbitrary straight lines pose their own problems-- though they look neat and tidy on a map, you'll note that such straight line frontiers are relatively new. Traditional frontiers followed natural boundaries of one kind or another -- a river, perhaps the crest of a mountain range. By stipulating arbitrary coordinate boundaries, surveyors were given a substantial challenge. Instead of "identifying where I am in a historically traveled space" they now had a problem "here's a coordinate somewhere across rivers and mountains: get to it and survey a line from it".
Surveying California's northern border with Oregon and eastern border with Nevada makes for amusing reading for anyone who thinks straight lines are easy in the field
Early in August, 1855, Mariette directed a civil engineer, George H. Goddard, to "determine the location of the California-Utah Territory line where it passes through Carson valley. Goddard established an astronomical station near where the Truckee River leaves Lake Bigler, calculated the intersection of the 39th parallel with the 120th meridian, but did not set a monument." This intersection is the defined "elbow" in California's eastern boundary, and it inconveniently falls in the waters of Lake Tahoe. Some 40 or 50 years later, Goddard recalled some of the hazards of that job, including "hostile Indians, who killed some of his animals . . . some of his party left him, and he remained with one man for some time to obtain a lunar' .
Speaking of California and Nevada, the boundary itself was ambiguously specified in documents like Nevada's Organic Act, leading to the so-called "Roop County War", and no end of challenges for surveyors, who had to figure out not just where they were, but just what coordinates they were supposed to be surveying. And then the people reading these surveys had to figure out what to make of them in the context of their charters.
There's also a substantial technical problem that coordinates for North American surveying had anomalies, assumptions made that were incorrect. In California v. Nevada the Supreme Court, no doubt enjoying a digression, in 1980 had to wrangle with a state constitution that assumed that the Greenwich and Washington meridians were perfectly offset, when they were not:
"Nevada's Constitution stated that its boundary would proceed "in a North Westerly direction along [the oblique section of the] Eastern boundary line of the State of California to the forty third degree of Longitude West from Washington [and then] North along said forty third degree of West Longitude, and said Eastern boundary line of the State of California to the forty second degree of North Latitude. . . ." Nev.Const., Art. XIV, § 1 (1864).
Although it turns out that the 43d degree of longitude west from Washington does not exactly coincide with the 120th meridian west of Greenwich—which was the north-south reference in the California Constitution—the Special Master concluded that the Congress that approved Nevada's Constitution was of the view that the two lines were identical. Certainly the language of the Nevada Constitution supports this conclusion by seeming to equate the 43d degree of longitude west of Washington with the eastern boundary of California."
One interesting bit of 19th century geophysical diplomacy was the attempt to standardize meridians-- both internationally and domestically. This enterprise was both necessary and filled with complications, depending on just when a line was surveyed, the imputed coordinates can have a different meaning with reference to the meridians which they specify. There was an international "Meridian Conference" in 1884, and more than a little wrangling, both over technical issues and political ones (the primacy of Greenwich being a sticking point for some nations, for example).
The meridian problem is a longitude problem, but you'll find that there are problems with the East-West baselines as well. Some of the East West boundaries are hundreds of miles long . . . at these distances, a straight line can deviate some distance from the specified latitude. The problem of latitude surveying was notable in the US Canadian frontier, although an ostensibly easier problem it took many years to survey. The International [in Canada] or Northern [in the US] Boundary survey took decades to identify just what in the terrain most properly corresponded to what was specified in Treaties.
Sources:
Woodward, Kay. "Chaining Oregon: Surveying the Public Lands of the Pacific Northwest, 1851-1855" (Macdonald & Woodward: 2008)
Landrum, Francis S. “A Major Monument: Oregon-California Boundary.” Oregon Historical Quarterly, vol. 72, no. 1, 1971, pp. 4–53.
Davis, William Newell. “The Territory of Nataqua: An Episode in Pioneer Government East of the Sierra.” California Historical Society Quarterly, vol. 21, no. 3, 1942, pp. 225–238.
California v. Nevada, 447 U.S. 125 (1980)
“The Meridian Conference.” Science, vol. 4, no. 89, 1884, pp. 376–378.
Pratt, Joseph Hyde. “American Prime Meridians.” Geographical Review, vol. 32, no. 2, 1942, pp. 233–244.
Carroll,Francis. "A Good and Wise Measure: The Search for the Canadian-American Boundary, 1783-1842" 2001
Lass, William E. “How the Forty-Ninth Parallel Became the International Boundary.” Minnesota History, vol. 44, no. 6, 1975, pp. 209–219.