Just a little bug that shouldn't take but 5 minutes to fix. I'm using the latest available beta of 1.6 available through Stardock Central. Here's the steps to replicate:

1) Get a spy
2) Open the Domestic Stats
3) Go to the Espionage tab
4) Choose to place the spy using the button in the bottom left
5) This will close the domestic stats menu and let you place the spy, do so to some shmuck civilization somewhere (I recommend Drengin, cause I always play Altarians and enjoy hurting them)
6) Click on Domestic Stats again

Nothing happens. The second click will open the Stats menu like normal, but the first one is apparently considered to be closing the menu, but the menu is already closed and so the game doesn't do anything.