I copied and pasted some of the lodestone graphics and put together some terrible looking bubbles, just to illustrate things a bit.
http://i53.tinypic.com/ajv2at.jpg
Say bubbles could change in size and opacity based on how far away from the character they are located. This would simulate depth.
Shout bubbles could pop in full size and full opacity. I'm thinking they should last less time in screen than Say bubbles.
If you ask me, it already makes that random googled screenshot I found a lot more lively than the chatlog.
edit:
Some more ideas.
When a character is targeted or a bubble is mouse highlighted his opacity could be set to full. Maybe even the bubble say if we are dealing with say.