A couple of things that would be nice to put in the game log:
1. When someone plays a Charm, it can be difficult to tell which mode they chose. A line saying which thing they got would be nice.
2. Before the first buy in any given buy phase, it would be nice if the log had a line printed in it, saying how many actions remained, the money and buys. This would make the logs much more useful. You could even consider putting the number of cards left in hand in there too.