I'd like to add that I was able to reproduce the bug by loading a saved game in ground combat phase during a new campaign.
Right after loading the save I was no more able to select my unit by clicking on him. Instead the game suggested whether I would like to move some kind of shadow looking thing from the left most corner of the map to the position of the unit I was trying to select. Again, as I did that, one of the units teleported into the shadows location and began moving.
Also all the aliens became visible through the "fog of war".
I tried loading the save game again and this time all my units, alive and dead civilians plus aliens appeared in the left most corner.
This seems to happen every time I load a saved game in ground combat situation.