I've had this a couple of times with a stuck animation (usually when a unit is moving through a city on a road). All the rest of the turn seems to play out normally, but it does not allow the turn to be completed, it simply returns to the unit in question. Saving the game and reloading moves the unit to the correct location, and the turn can be continued.

Haven't been able to catch this one in a repeatable save file, but my hunch is that I've clicked on the exact tile that the unit SHOULD end up on, and the animation glitches upon exit of the city.