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...

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?