If you are seeing events that seem to be out of order (eg. a person takes a move after being removed from the game), then it's likely you have a connection issue to BGA.
Multiplayer systems are hard. Most developers stop working on something once they get it to work, but some developers continue on and test what happens with different types of lag. A really well designed system will have some kind of feedback to the end-users to let them know if their connection is solid. BGA doesn't do this. Your best bet is to reload the full page again (F5 or ctrl-shift-R), and that should show the current stage of the game.
Some games on BGA may have errors after reloading. When the front end is fully reloaded, it will build the current game state for the user using different methods than if you arrived at the same point by playing through the game (without reloads). But these types of errors are easier to catch, and it's pretty rare that these errors exist after the game has made it through alpha and beta.
So.... if you think you see continuity bugs like this, and you see them regularly, it may be that your connection is particularly bad. There could be a hard to detect bug where the front-end state can be wrong, but only in cases of extreme network lag. You may be the person who can detect it and figure out what exactly is happening. Take screenshots before and after hitting F5, and then file a bug, once you are sure it is a bug.