Let's say I have a failed invasion, leaving many dead stones. For every move I make there is an obvious counter. However, say one such move captures a stone. I capture, white responds. My extra lost stone is balanced by my opponent playing in her territory, but does anything balance the stone I captured, or is that an extra point (under Japanese scoring)?
When your dead group is removed, your opponent will have an extra point of vacant territory, because the stone you captured (which would have been filling one of his points of territory otherwise) is no longer there. This balances your capture of the stone.
Yes, but white also responded, costing her another point.
black loses a point for playing a dead stone
white loses a point for playing in her territory AND
black gains a point for a captured stone
1. Black loses 1 point, the stone he added 2. White loses 1 point, the stone she added -> balanced 3. Black wins 1 point, the stone he captured 4. White wins 1 point, the intersection under the stone black captured -> balanced again
I had the same mistake in thinking some months before. Just don't forget: if you remove a white stone out of white's territory, the now free intersection is one more point of territory for white.
Reuven - However don't forget that you might be able to get extra points with a dead group if the opponent is forced to remove it by playing at the end of the game, see Semedori.