The bugs I ran into so far:

• Quest: "What a good idea" counts visiting the same system two times as two seperate system visits.
• The game crashes upon starting a landbattle vs a minor civilisation if I pick the infiltration option.
• I was building a "Trade Company Subsiduary" in two different systems at once. Once one of them is built, the other would take infinite turns to complete. You should instead not be able to build two at once if it is above the permitted limit.
• The right click function doesn't work as good as it should; Clicking in some places doesn't work.