When there's a stack of ships/fleets in a hex something doesn't feel right.
Attacking a stack of enemy ships seems to be when weirdness begins. I've observed explosions appear in empty hexes (perhaps last battle area). Movement appears to stall. Just generally wanky feeling--hope that's not too technical. 
If I'm working my own stack of fleets, I don't see a way to "Pass" on an idle ship or fleet in the stack. I end up moving something out of the stack so I can "pass" on it.
At least once, I _think_ I was getting an "Idle Ship" notice, but clicking on it took me to a stack and none of them had any movement left. I believe I disbanded the fleets and was able to continue.
Not related to stacking, but I also had an Idle Planet notice for an invaded planet that was difficult to get rid of. I had placed something on all the tiles to build or upgrade immediately after the invasion rather than waiting for the Idle Planet to take me to it. So perhaps some test/check is out of order or not updated at an opportune time. I think I ended up changing the world's production orientation back and forth to get the Idle Planet notice to go away.
--David