http://gyazo.com/7fdbf7003e469125dd8b53ff91a1cd4f.png

:<

How can I get the edge of this texture to align properly without changing the texture scale? Notice how there's a bit of black left past the white line.

Thanks in advance.

Hold down ALT while dragging. This also goes for angles when rotating.
A perfect alignment can be had by left clicking the adjacent surface and ALT+ right clicking the surface where the texture is supposed to be applied to (while in Face Edit Sheet!). Requires the brush to be on grid.

EDIT: I forgot to mention that you generally shouldn't create/size world brushes off grid without a good reason (if there is any). It is much better to keep everything on grid and if I'm not wrong compiles faster.