When detonating a large stack of TNT as part of a New Year's finale on a private server, no other players on the server saw the TNT explode or the resultant destruction. Other players could still interact with the destroyed blocks as if they were still there, while on my screen they clearly were not. Only after quitting and rejoining did others see the carnage. Not sure if related, but there was a fireworks show on at the same time from dispensers activated by minecarts.