My stats seem more reasonable to me on a single world and not a whole account. Could we either change them to be per world or have an option across the bottom that would switch it between account and world.
I've thought about this recently too.
I think stats could make sense on a per world basis, and then there'd be an overall tally as well.
Achievements, I'm ok with just being overall. I really don't want to be doing them multiple times.
Some other things that I wish were on a per world basis? Textures and the difficulty level come immediately to mind.
I completely agree that both stats and achievements should be specific to the world. My stats are messed up because I have both survival maps and editor maps (e.g. I have a puzzle map in progress, so it says I places several thousand smoothstone). Achievements have much the same logistics; they're supposed to introduce people to new worlds, after all.