There's also potential for the 3rd Edition problem where a high level fighter had a higher chance of critical failure than a low level fighter.
What is this "critical failure" of which you speak?
I mean sure, you can add a house rule for critical failures, and I think it might have been an optional rule discussed in one of the sidebars (p. 28 of one of the DMGs, apparently; it comes with a lot of cautions, even then), but core 3.x editions didn't have any fumble mechanics. A natural 1 was an automatic miss on attacks, but it didn't carry any additional negative effects.
If you did add such a house rule, it might behoove you to also add in some sort of confirmation roll similar to that required for a critical hit. (So natural 1 --> roll again --I'd recommend at full normal attack bonus-- if a miss, then you have a critical fail; I don't care for the DC10 dexterity check in the sidebar I mentioned.) You might also rule that only the first or last in an iterative sequence could be a critical failure, meaning that there is only one chance to fumble per round regardless of your iterative attacks.
If you have fumbles (that do something meaningfully bad to the fumbling attacker), then the critical hits should be more meaningful, too, and not just extra damage. They should also occur much less often, in my opinion, than 1-in-20 times (modified by whatever confirmation rolls you have in place). More like 1-in-100 or 1-in-1000, or even less. If otherwise, then combats between (semi-)trained (quasi-)professionals becomes (once again, in my opinion) a bit too slapstick.
In general, this points to why I am not in favor of such house rules. I think fumbles should be left out. (Except possibly for weapon breakage in Athas, and I liked the 4e version there, making it a player choice with some benefit added on to tempt the player to make that decision, upon occasion.)
Just my thoughts.
Edit to add:
And to address the OP, I like what I've read about the Combat Superiority dice; it's the one of the most interesting things I've seen about Next, so far. IMO, of course. I'd like fighters to have this sort of interesting choice to make each round.