Why are all the claims square?
The truth is: they aren't. Mine sizes are limited, so holders only file mines for the land that they want. The mine is then plotted out according to the Public Land Survey System (PLSS). PLSS maps locations by square plots of land rather than the points defined by latitude and longitude with which most people are familiar.
The BLM references mines according to the PLSS. So when The Diggings™ gets their records of mines, the smallest unit of measurement provided for these mines is a Subdivision. This is the same degree of accuracy that you would find with the LR2000.
These subdivisions contain the mine but are not the exact outlines of the mine. More accurate mine maps are available, but only through the regional Information Access Centers run by the BLM. If you are looking to file, buy, or sell a mine, it is important to go to the relevant regional office to get copies of the official mine records.