How do I know how many tiles I've seen?

Solution 1:

As taken from the WildShadow Forums:

Tiles count as "seen" if they are filled in on your minimap. The circle of "seen" tiles on your minimap has a radius of 16 tiles. You can do the math from there.

Otherwise, NO, you cannot see your current tile-seen count at all.

Solution 2:

Use Muledump. It is easy to set up, but read the instructions carefully.