Non-linear scale of ammeter?
I think whoever made that claim was somewhat confused. Galvanometer-based ammeters are pretty linear. He was probably thinking of "moving iron meter", which is indeed non-linear; the deflection in those is proportional with the square of the current, so the screen might look like:



The difference in linearity between galvanometer and moving-iron meter these is owed to the fact in the former the flux density is constant, while in the latter, the movement of the iron increases the flux, so it's a form of positive feedback if you like.

It's actually possible to manipulate the geometry of the coil so that the moving-iron meter is somewhat linear in parts of its scale, as shown on this Wikipedia example: