I just lost an assault specialist because I didn't realize two enemies were on overwatch. Was there something I should have noticed that would have told me they were on overwatch?
I'm fairly early into the game but if an enemy is in view during their turn you can see when they go on overwatch. It pops up on the screen that the enemy has entered overwatch. I assume this is only for enemies in your view and that it doesn't constantly say it over their head thus forcing you to remember. I'll have to check somehow.
UPDATE: After playing the game for a while I've seen a lot of enemies go into overwatch. There is no way to tell they are in overwatch until they fire unless you see them. You need to remember what enemies are doing what.
If you've never seen the enemy they will not be on overwatch when you first see them; they have to move into cover (not necessarily for berserkers and floaters, but they still move). Otherwise, if you've seen one and they move back into fog, you can't tell if they are in overwatch unless you have sight, though if you wait a couple of turns that might give you a clue, but this is also not 100%.