What I love especially, is that he is very careful and systematic about his conclusions, splitting up in cases, instead of simply producing the solution and then proving it is a valid solution.
For example he does not assume that every point in space has a single value for total potential. First he describes how it is at least theoretically conceivable to follow a path and observe the total potential to vary continuously, and arrive back at the point of departure but end up with a different value of the total potential. He is effectively describing the possibility of wormholes (which didn't bear the name "wormhole" yet back then), or "charge without charge" (think Wheeler). But after this part of the book he assumes that the total potential is singlevalued (not because he proved so, but because describing physics in spaces with complicated topologies is far from straightforward, even today).