There is a street that is split down the middle by the USA-Canadian border, aptly named Canusa street. People who live in houses on the south side of the street are in the USA, and the north side, in Canada. Crossing the street requires having to report to the border crossing office.
The US had to abandon construction of a border fort in New York State after realising that they’d accidentally built it on the Canadian side of the border. It was promptly nicknamed “Fort Blunder”.
Märket is a tiny island divided by the Finnish-Swedish border. When the finns inadvertedly built a lighthouse on the wrong side of the border, the swedes agreed to trade it for an equal spot of land on the other side, causing the border to zig-zag.
The US-Canada border is the longest border in the world without a military defense.
It is possible to walk from US soil to Russian soil from December to June as an ice bridge forms between the Diomede islands.
Denmark has a navy unit that patrols Northern and Eastern Greenland to enforce Danish sovereignty over these regions.
There are robotic turrets guarding the border of South Korea.