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...

As an excellent example of #2 we've got Bir Tawil and the Halaib Triangle - both exist along the Sudanese-Egyptian border. Two different historical border drawings have been presented which each argue that the Halaib Triangle belongs to a different country and the triangle has 27k inhabitants. Funnily enough, each map that yields that valuable chunk of land to each country actually yields that Bir Tawil should be possessed by the other country (and Bir Tawil is comparatively worthless). As a result neither country claims Bir Tawil since it could be seen as an admission that the other country has a rightful claim to Halaib Triangle.

Usually these weird chunks of land that lay unclaimed are usually the result of agreements or contests around more valuable chunks of land that cause voids in the border - sometimes just due to historical oversight.