In the first Go 19 Championship has just finished a game between Dong Wei and Rudolf. The first one should have won the game after my calculations, but they made some scoring mistake and the second got the win.

This result has a little influence on the 3rd and 4th places, but that's not the point. What should be done in situations like this? Or what can be done?

Under Japanese rules, the result cannot be changed under any circumstances after both players have confirmed it (Article 10 Clause 4). So, since Little Golem uses Japanese rules, the result in game #1037 has to stand.

There are other examples of mis-scoring, see for example game #5034 (which affected who got through to the next round of that monthly cup) and game #9582.

Game 5034 is clearly won by white as the result says… :-)However, the other one is miscounted.

I don't understand your comment about game #5034. As far as I can see, it should have been a win for Black by 1.5 points. (Black has 18 points of territory and 5 prisoners. White has 15 points of territory, 1 prisoner and 5.5 komi.)

Ooops, i'm sorry, i've added the prisoners backwards :-)