Yeah, a dirty applicator means it wasn't really clean enough for LSPing, oughta use something like Sonus green clay first.
The direction won't matter with regard to inducing marring, PCs move in "random orbital motions" and nobody says that *they* oughta be moving in straight lines. Straight line scratches aren't as readily visible as circular ones, but you shouldn't be scratching when you wax anyhow.
Work at getting an even application, it just takes a little practice. I too generally wax by machine, but I apply sealants by hand and it just takes a while to get the right feel for certain products.
But I bet the whole thing would go better if the surface were better prepped. Get rid of whatever's causing the soiled wax applicator and I bet you'll also get a better looking wax job. On a well-prepped surface, as the was dries a certain amount of wax bonds and the rest gets buffed away, it's almost self-regulating.. but this depends on how well-prepped that surface really is and you do need to apply a reasonably uniform amount of wax.