A friend and I played our first game with basic rules and I had a similar question. We didn't realize that you continuously perform spotting throughout the turn. After rereading a few rule sections and this thread I think I understand it.
Is my understanding of this correct? A vehicle in a clear hex with no Spot markers and LOS is spotted by a unit with LOS 20 hexes away. If that vehicle is given a Move command and moves one hex into regular Woods (also 20 hexes away and with LOS to the spotting unit) it is given a Spot/Move marker. That vehicle is still spotted because the -2 from Woods and +2 from Movement cancel each other out giving you 20 hexes again. However, if the vehicle first moved behind the woods to break LOS, he would not receive the Spot/Move marker because he broke LOS and thus is no longer spotted. He could then, during the same Move command, move into the Woods and only have a the -2 modifier and continues to not be spotted by the unit 20 hexes away with LOS. So in this situation, if the other unit was also a vehicle and he was in Clear terrain, the vehicle in the Woods could spot the vehicle in Clear terrain but not vice versa.
No, the unit is still marked with a Spot/Move marker. The fact that it moved behind the woods and then reappeared does not mitigate the spotting. How else would a unit be spotted that was behind woods and then moves into view during the movement phase?
I stated earlier that Spot counters are only removed during the Spotting Phase, not during a turn. That way, it's much easier to keep track of who is spotted or not.