Coin Flips and Time
So I just went against a Celebi ex/Serperior deck and the opponent flipped 10 coins. As soon as the damage was dealt (and my Pokémon fainted) I was prompted with the timer countdown saying "hey, you need to select a replacement in the next ten seconds" because despite the animation continuing on my end to flip coins, the flips and animation had already happened for the opponent, so it was considered "my turn."
One or two more energy on that Celebi ex and there's a chance I wouldn't have even been able to select the replacement myself and the game would have auto selected something that could have lost me the game.
The animation either NEEDS to happen for both players at the same time, or the turn NEEDS to start AFTER the animation for the player on the other end.