1. The Four Corners monument marking the spot where borders of Arizona, New Mexico, Colorado, and Utah meet. Even after several lawsuits and court rulings, it's still off by half a kilometer or so.
Reading the Wikipedia article, it appears that the monument is off from its originally intended position, but that it has been confirmed by the courts that the surveyed markers supersede the written descriptions and therefore define the border. In other words, it makes no sense to say that the four corners marker is misplaced as it is by definition where the corners meet.
Another interesting example of marks and boundaries in the physical world superseding surveys and agreements is the USA/Canada border west of the great lakes. While officially the 49th parallel, the border was manifested in the real world as a series of straight lines between hundreds of monuments. These were set down without GPS, and at times wound around obstacles, so there's a fair degree of variability in how close these monuments actually are to 49deg: http://www.confluence.org/country.php?id=3#NOTES
The zigzag is actually fairly easy to see on Google maps, because the border is maintained by both the US and Canada, clear cutting the lines in forested areas. This highly visible physical boundary is the true national border.
Reading the Wikipedia article, it appears that the monument is off from its originally intended position, but that it has been confirmed by the courts that the surveyed markers supersede the written descriptions and therefore define the border. In other words, it makes no sense to say that the four corners marker is misplaced as it is by definition where the corners meet.