My current favorite boundary dispute is between California and Nevada.
California entered the union in 1850 and it's north-eastern boundary was defined a specific way(120 degrees west of Greenwich), Nevada entered 14 years later and it's western boundary was defined with a different method(43 degrees west of Washington), at the time it was thought these two methods were equivalent, but this was later proved otherwise. It appears the main strip got resolved but there is still a weird triangular strip of land on the diagonal claimed by both sides. There were also a number of surveying mistakes, but the root of the problem appears to be the accepted but incompatible definitions. It turns out that congress has no authority to change state borders once they are set(Somehow this both surprised me and made total sense at the same time), so the states themselves have to resolve it. There is currently an "agreement" on how to interpret the border, but neither state has changed it's constitution so the dispute is still technically ongoing.
https://en.wikipedia.org/wiki/Lake_Tahoe#Interstate_boundary...
Reading the constitutions of both states in order to pin down exactly where the problem is, the Wikipedia article is sort of vague. The Nevada document specifically references "thence in a North Westerly direction along the Eastern boundary line of the State of California to the forty-third degree of Longitude West from Washington" So that is not the problem, the border is whatever California says it is. It must be a north-south strip in the difference between "the forty-third degree of Longitude West from Washington" and "Running south on the line of said 120th degree of West Longitude"
The latest California constitution just says to reference the original 1849 for the boundaries https://archives.cdn.sos.ca.gov/pdf/1849-california-constitu...
Nevada https://www.leg.state.nv.us/Const/NVConst.html#Art14 amended in 1982, but the original 1864 document has the same geographic description with a different starting point for some reason.
The funny thing I found in the Nevada constitution was
"All territory lying West of and adjoining the boundary line herein prescribed, which the State of California may relinquish to the Territory or State of Nevada, shall thereupon be embraced within and constitute a part of this State."
We reluctantly agree to your existing borders, but we really wanted the Sierra Nevada ridgeline to be the border and if you want to give it to us we are going to put it right in the constitution to accept it. The passive aggressive tone in such a formal document just kills me.
Wait, so it was actually believed that the Washington meridian just happened to fall exactly on an integer number of degrees (120-43 =77) west of Greenwich?