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.