[lmkg]

From the example notations that he gives, all three Einstein notations as well as the Penrose notation make the indices explicit in a way where a mismatch or misalignment will stand out.

Another good example is the Liebnitz notation for derivatives. Proper application of the chain rule visually resembles how fractions cancel: dy/dz dz/dx = dy/dx. It's very easy for the eye to follow and make sure that the cancellation is valid. Newton's notation doesn't make that as easy.