Trigger Scenery is dependent on whether or not Trigger Crate or Trigger Zone is used. A Trigger Crate, when hit, affects the trigger scenery for all players, including the host (which of course means that all players joining the server thereafter continue to be affected by the trigger), while a Trigger Zone, when touched, only affects the player touching it. I'm guessing why this happens is because a Trigger Crate is spawned as an object, and objects in MP, when taken or destroyed, is updated for everyone in the server.

Destruct Scenery is supposed to be a server wide event, but during many games of Ground Force it's not at all uncommon to see someone standing on air. My guess is that the server sends information about what blocks have been destroyed, the client misses it due to packet loss, then the server stops sending information, leaving blocks available to the client.

My take on the other two Sceneries is that they function more or less the same way as Destruct Scenery. Bomb Scenery is rarely used for actual destruction, but as a wall of sorts to prevent ammo going through walls and taking power ups which are meant to be physically visited.

Animations start when a player loads a level, so these are not in sync.

MCE Events and other generated objects have their presence announced to the clients by the server, and are probably treated like any other object.