Hey Enkhidu! We've played together at the Ohio ENWorld Gameday if I recall, and you may have seen my spreadsheets for 14th level characters and monsters that can "auto calc" rolls, including all the appropriate benefits (Assault on the Fire Giant's Citadel). It is, however, an ENORMOUS task for the DM to keep track of, and more importantly, prepare for. This time will eventually deter from your ability to focus your time on building the even more complex and layered stories your players deserve!
If you are blessed with the good fortune of gaming with fresh-minded, game designers, you may have no problems. Otherwise, for the majority of all other D&D players, the wheels completely fall off the game above 12th level.
How bad does it get? There are 49 conditions that affect combat and 144 modifiers to those conditions. You can't remember all of that in your head? Come on!
That's not even factoring in types of attacks, # of attacks, attack bonuses, armor classes and armor class modifiers, damage, and damage modifiers. I think you get the exponentially worse picture. There are some big opportunities to improve it. (For my fellow analysts and managers out there, yes, I actually process mapped D&D combat.)
Suggestions: well, first and foremost, make sure your group is committed to making this work. It will truely need to be a team effort. Everyone will have to do a little more work to make things go more smoothly. Second, I've found an excel spreadsheet to be a DM's good friend. Finally, I recommend talking to your group about combining and limiting the hundreds of effects that can become a real pain to keep track of at this level. For example, what if all morale, luck, sacred, divine, competence, and size bonuses were combined into a more generic "buff" bonus, and these bonuses generally lasted for 1 combat. It makes life a lot simpler for everyone. It's not like the party or the DM will be lacking for ways, but it prevents everyone from being forced to cast 12 different spells and do hours of research to find that one optimal combination, and keep track of each modifier separately. Same thing goes for the myriad of defensive capabilities - armor class, resistances, immunities, cover, concealment, displacement, blinking, and damage reduction. It will become very complex, very quickly if it hasn't already. Streamline this as much as possible, using the same "simplicity" approach as with buffing. Near the end of the campaign, and as you enter epic, there should be pretty standard "defense arrays" available to your players, when in various states of preparedness.
I hope this helps. Let me know what you've tried, and what works! This is an area of particular interest to me, and I'm trying to help pull together the best practices that can be used to make the game better at high levels. I'll be testing some of this at Origins this year (under Myrik Games). Hope to see you there!