While Dom is really fun and I have well over 900 games played of it with combined W/L games, I do think there are a number of problems that need to be looked at that I believe would make Dominion even better. They are...
1.Bot Lane
2.Revive
3.The Respawn Timers
4.The Quest System
5.Items
1. Bot Lane
I can identify one big problem with bot lane in Dom. Hardly anyone wants to go bot because its not as action oriented as top, which causes some people to look at it like a chore. To be honest, I don't blame them. Sure bot lane gets ganks and some action, but it is nothing when compared to top lane where a lot of the action is at top lane, the jungle, and the Storm Shield.
I would like to hear other people's suggestions on how to solve this because the only one I can think of is rather major change (a complete rework of the map). though ill tell you anyway what it is.
I believe what can help this problem is instead of the circle formation, it could be a square formation with the mid point being in the middle of the map. Think of it as a square with each point at the corners and the middle point in the mid which is connected to the other points with a X formation. Of course this is a big change and would need a rework for the Storm Shields, Speed Shrines, and jungle placement. I would like to hear other suggestions for this because mine is rather big and would require a lot of work.
2. Revive
I see the high usage of revive to be a problem in Dom. It just gives to much in Dom to not take it. It revives you, gives you health, and a speed bonus for a short duration. You mostly always want revive over any other summoner spell. This is not healthy for Dom because it limits players choices to one other summoner spell because revive is almost always needed.
What would I do the fix it? Remove it as a summoner spell and add it somewhere else (Dom only). While its not good that everyone takes revive (as I pointed out) the gameplay its creates is rather fun and makes Dom more enjoyable. I would rework the Dominion UI to have a button that gives each player X charges to revive. After you die, you can use one of the charges to consume it and it revives you (no HP bonus and lower movement speed bonus). This would not only keep the gameplay that revive brings to Dom in, but it would allow us to use two different summoner spells which is more healthy then using revive and something else.
As for if these charges should have a X minute delay for each other, that can debate. I personally feel there should be a 2 minute delay between each use, but they both have pros and cons. I truly believe this is a really good solution to this problem.
3.The Respawn Timers
Nothing bothers me more when i am bot and both me and my enemy kill each other. Then I go see that he has a much less respawn time then me. I have heard that a losing team gets a faster respawn time, a winning team gets a slower respawn time, or something like that. I am not a fan of that personally.
4.The Quest System
I made a post a while back about this, but ill sum it up here.
1. Quest Placement
There is not enough variety in the quest placement. Having a quest spawn top and the other teams mid, its not really fair most of the time. I would like to see quest not spawn at top and instead do one of three things.
Spawn at both mid points, both bot points (which i know we have already), or spawn diagonal to each other. This would be much more fair then have a quest spawn top.
2. More quest types.
I really do like the concept of quest system, but it can be worked on a bit more. I would like to see more then one type of quest, and like i said in my old thread, I would also like to see two different types of quest spawned at once. When you cap one, they all disappear.
Here are some suggestions for different types;
1. If my revive suggestion was added, make a quest give another revive charge.
2. Make a quest that "locks down a point" for a few seconds.
3. Make a quest that increase movement speed by X percent for X secs.
4. Make a quest spawn that lets the point spawn a stronger minion if captured for X times.
That is just a few ideas and yes if the numbers are off, they can be really broken. But the same could be said to our current quest, which gives percent damage increase. I think if the numbers are right these can work. Of course if anyone has suggestion for other quest feel free to share or criticize mine. 
5.Items
Ok this is pretty simple and I know its coming, but I would like some more item. Like more items that give vision like sweeper, (i am looking at you Soulsight Lantern, of course build differently because we don't need bonus damage against minions in Dom) and maybe some more items that give vision for HP and other stats. I know Dom will be getting new items, so this did not have to be long. lol
Anyway that's all my suggestions and it took me a very long time to write this all. If you read all this (congrats lol) leave me some feedback and other suggestion you might have.