Some interesting thoughts.
I want to add mine as well. Albeit they'll be from the perspective of one who hasn't actively done Arenas since TBC, so keep that in mind :)
To me the biggest problem with Arenas is the repetition. Because Arenas are so focused around strategies, there's even less opportunity for dynamic play compared to Battlegrounds.
And at least for me, after 2½ Seasons in TBC, I thought I had seen everything Arenas were about, so why bother spending time on additional Seasons?
There has to be something that helps break that feeling of "Oh, Nagrand Arena again, and it's another RMP - do as usual".
I think Mists of Pandaria's talent system will help a little bit with that, because you won't know what talents your opponents have until they use them.
But I also think Arenas need new maps - and many of them. In StarCraft II Blizzard adds new maps each Season in order to challenge players and force them to think of new strategies and ideas. Likewise, for raid bosses in WoW, Blizzard keeps introducing new mechanics that challenge players and force them to learn new things and come up with new ideas.
The same should apply to Arenas in WoW. The act of running around pillars is getting old. I thought it was old by the end of Season 2 in TBC, and now we're in Season 11 and it's still about running around pillars, because it's the same maps people are playing on.
I also think that Arenas don't feel like they're part of WoW.
This is probably not a concern for those who play Arenas entirely for the competitive aspect of it. But my desire to do anything in WoW builds on my love for that which is Warcraft. And when you look at Arenas, they don't show off much that has to do with Warcraft.
I miss an Arena environment more akin to that of Trial of the Crusader. I want crowds spectating and cheering when someone gets killed. I want a Tirion-like shoutcaster who starts the game - rather than a dull countdown timer. I want a ton of different, adrenaline-pumping battle music that makes me feel like a true gladiator in each battle, rather than the theme park visitor who queues up for the same rollercoaster again and again. I want the game to show me my victory, be it in the form of lots of fireworks, being showered in flowers from beautiful Night Elves, or just a pat on the back - anything but having a boring scoreboard with hardly any information on, covering up the epic scene of my dead opponents lying at my feet. Talk about an anti-climax.
And where is all the story about Arenas? I loved the way Thrall's story unfolded as he was being used as a gladiator in Arenas by Blackmoore. And I loved how Varian....or Lo'Gosh, thrived in the Arenas during his captivity, and how the Orcs around him were just in it for the sport and the money it made.
It shouldn't be so hard to implement a story about Arenas in WoW that progressed as each Season unfolded. For crying out loud; TEH GLADIATORS WoW comics are able to do it, so surely Blizzard can as well - especially given the fact that they have already done so in their own novels and comics in the past.
That total absence of anything Warcraft-related in Arenas is a huge issue. Why would I, as a Warcraft fan, spend any time in WoW on an activity that has nothing to do with Warcraft?
The reward structure of Arenas is in a terrible state as well. The problem is that as far as rewards goes, Arenas only appeal to the best players.
What rewards do you get from Arenas if your skill-level is ~1400?
Achievements? Nope. They're all about progressing your rating to high levels.
Gear? Nope. You earn the gear you need to be able to compete - the tier 2 gear which is the bonus, is out of your reach.
Titles? Nope. They're for the high-ranked players only.
Mounts? Nope. High-ranked players again.
Anything else? Nope. Nothing.
That isn't good enough.
The reward structure of Arenas needs to be more akin to that of Rated Battlegrounds, so players can earn something, even if they're not God's gift to PvP. The player simply has to end up feeling that the time and effort spent doing Arenas was well worth it, even if he or she didn't manage to acquire a rating above 1400. That player should still have earned a mount or a title, or something, for the time and effort spent - otherwise that player won't bother with Arenas in the next season.
And for high-ranked players, there also has to be more to the rewards than the prospect of a flying mount (which you can't use in Arenas - talk about adding injury to insult :P), an increasingly dull-sounding title, and an item set with an "exclusive" color theme.
That is pityful.
Does anyone envy the Gladiators that faaaantastic prize pool? Hmm...nope.
I can take my newly-dinged level 85 alt, join a PuG run to Icecrown Citadel, chop through the achievements there, and earn a mount and a title that's way cooler, and I probably get a lot of cool items for transmogrification in the process. And it won't even take more than a few hours. Why would I bother trying to become an Arena Gladiator when I can do that?
And finally, the way you do Arenas needs changing as well. It's only for Arenas that players still need to organise teams/groups beforehand. I can queue up for random dungeons, battlegrounds, and raids, but not Arenas. Why?
Arenas need the equivilent of the Random Battleground queue system. I want to be able to simply queue up for the Arenas on my own, be paired up with two dudes I've never seen before, fight against a team of three other random dudes, and earn a little honor for doing that.
I don't want to be part of an organised Arena team in order to be able to do Arenas, because my schedule is already packed as far as time commitment goes when it comes to raiding. I don't need more of that - I need less.
Think that's about it.