Only when I detect by sight do I veer diagonal. If I can find mower lines in the turf I'll use those as a reference.
Sometimes I grid in tight overlapping alternating circles that spiral outwards. I find it more effective than straight gridding, and the ground gets swept from many angles. Takes more time though.
No, but sometimes if i'm looking for an ornery target and iv'e been crouched down for a few minutes, I will get back up and walk the way I just came from ! Lucky for me it only takes a split second to realize I need to turn back around.