I manually explore in the early game because auto-explore is weak as the OP describes. But I'm kind of compulsive about wanting a complete map, so once I'm more or less finished planting colonies, I turn on auto.
The sloppy close-in work doesn't bother me nearly as much as when an exploring ship decides it has to head for the opposite side of the map despite the large swaths of unexplored territory much closer to home. I show auto-pilot lines on the mini-map, so those decisions are usually easy to spot and then I do roughly what the Capn says and try to manually put 'em somewhere that won't tempt auto-explore to be super stupid.
Sure wish I could train the little boogers.