As it stands the Combat window is very, very limited. Due to the amount of information it displays it will often result in not only information overload but insane scroll speeds that can make the chat almost if not entirely unreadable.

My suggestion is simple. Implement more filters for:

Buffs gained.
Debuffs gained.
Healing taken.
Healing given.
Hits absorbed, both by you and against you.
Damage and with the ability to color code by type.
The equivalents for pets, party members, and raid members on an individual bases so that, as an example, a tank could see incoming (and in the case of Justicar tanks outgoing) healing for the entire group/raid while also tracking damage.

I would also like to see us able to spawn new Combat windows as well. As it stands every new "chat" window I open is just that, a chat window. That these also allow for system and game messages is pointless as they don't display combat messaging. Having a window open for healing and absorption to track self-healing and absorption from things like the Divine Defender's procs that don't track all other combat metrics would be great. It would give me a solid chance to help gauge the defensive side of a new build for my rogue. By the same token it would allow me to more accurately gauge incoming non-physical/white damage on my tanks.

This would also free me up from trying to pay attention to what mobs are casting or constantly trying to look at their buffs while still letting me get a rough guestimate (until addons or parsers come out that will appropriately track these metrics) which resistances are most important in a given instance.

In short, more options and ability to split up incoming data when in combat please.