Blizzard applied some hotfixes over the past few days that should help make the maps less of a circus. The gates have been removed from the Ring of Valor, allowing players to engage as soon as the problematic elevators hit the arena floor. The moving pillars were adjusted to start the match in the elevated position, whereas they used to rise a few seconds after the match started. Most importantly, the damage from the flame wall was changed to break certain effects such as Fears and Roots after a certain amount of damage has been dealt. The last change is nice, but it's still problematic. The only thing that should damage another player in an Arena is another player.
They also have some changes planned for Patch 3.1, such as bug fixes for falling through the world (gotta hate that), and making it easier to plan around the events in the new Arenas. As gimmicky as they are -- and they're gimmicks, make no mistake about it -- Blizzard intends players to plan their strategies around the events such as the waterfall in the Dalaran Arena. So they've made these events easier to identify and prepare for. Blizzard poster Mumper says that most of the changes are taken from feedback on the forums, which is great. They seem hell bent on making these maps work, so even though I think the moving parts and fire (stupid, stupid fire) are terrible ideas for an Arena map, their constant tuning helps make things easier to swallow.