Below are several bugs I have experienced in playing a couple of games of 1.31 (custom race, gigantic map, 9 races)
With the AI on Genius setting, they are setting up their Economic capital on planets where they have mainly put factories - surely this should be a manufacturing capital!
The movement of ships is very slow when the planet/ship sub-window is open and you have a lot of ships - each single ship movement point takes a couple of seconds rather than all movement taking a couple of seconds, as happens when a ship moves and the sub-window is closed. I notice that information on this sub-window is updated immediately (as each movement point is spent), perhaps it is not doing this as efficiently as it could. This problem is particularly annoying when you are trying to manage many ships, such as producing a lot of transports and not launching them until you are about to declare war, the only way to launch all the transports is to go through them one by one on the ship/planet sub-window.
Now and then clicking on a ship on the ship/planet sub-window does not take you to the ship in question but to a freighter - I think this happens when a freighter service stops due to war and it then misbehaves in a couple of ways. The other in when you click on a freighter that has stopped running, and I get a zero value ship icon window, together with the freighter icon, but no action could be taken on the freighter.
Now and then the little window showing a ship icon and its size value such as when the ships are stacked, is blank, except for the value.
I have also experienced the sticky map problem where it thinks that you have the muse button depressed but it isn't.
Now an then it takes a mouse over as a mouse click such as on the number selction bars, especially the tax one and a couple of others.
I did not notice any of these bugs in 1.30A, although 1.30A did crash on me a couple of time and 1.31 hasn't done that.