Uncanny Dodge: This is required for the class to actually work. Possibly add it as a prereq? I currently see Rogue 4/Fighter 2 or Barbarian 2/Swash 3 as being obvious lead-ins to the duelist. Warblade would obviously be a good fit as well, but hard to see someone choosing this PrC over some of the fine ToB Duelist PrCs if they went that route.
Okay, thanks for confirming what I was thinking. I do think having it as a prerequisite makes the entry a little too restrictive though. I think slipping it in at Duelist 3, where currently all you get is Fancy Footwork, would work, though.

Duelist Challenge: Does it require an action? Am I limited to only one challenge? When does the challenge end?
It is intended to be a free action to designate, once a turn, can have only one, and lasts until the enemy is dead or out of LoS. I guess my description didnt actually cover any of those things though, so good catch, I will update accordingly.

Perfect Opportunist: Not a fan. I like the concentration bit just fine, but not buying into the fact that every attack even successful attack generates a riposte. How about something like:
Well, the same thing comes from a feat... Robilar's Gambit if I recall correctly.

Clever Opportunist: At 9th level, when a foe provokes an attack of opportunity a duelist may initiate a disarm, trip, or bullrush maneuver with a bonus equal to your intelligence modifier on the opposed check. This maneuver counts against the number of attacks of opportunity allowed in one round, but doesn’t provoke an attack of opportunity or generate any negative consequences on a failed attempt. Additionally any concentration check invoked by an attack of opportunity from you has its DC increased by your duelist level plus intelligence modifier.
Problem I have with that is Trip, Disarm, and Bullrush coming from a (typically) medium creature using a one handed or light weapon with low strength is going to have really low checks on those maneuvers, even with the int bonus added to it. Maybe making it +Duelist Level + Int Mod on those as well could make that workable, though it'd still be pretty weak against most monstrous opponents.

Penetrating Strike: I like the ignoring DR and Crit immunity parts just fine, but not buying into the power attack by a different name bit. Most fighter types rely on PA for their damage; I think the duelist should do his business in a different manner. With the greater Penetrating strike bit you’re a better power attacker than the greatsword barbarian.

Maybe give the class Improved Critical and as a capstone double the Crit Multiplier. This will still up the damage generated, but help keep the class a bit distinct.
Fair enough, my thought was though that instead of gaining damage through raw strength, the duelist could essentially make a called shot, taking a penalty to hit to gain increased damage. And yes, the increased damage at max level exceeds that of a level 1 greatsword barbarian, because that greatsword barbarian still has advantages in terms of damage that the Duelist does not, namely the 1.5xstr to damage. And of course once you look at somethign past 1st level you likely have more Power Attack multipliers which brings the Barbarian's far above the Duelist's.

Now, if we wanted to go a different route, personally I wouldn't use Improved Critical as a bonus feat (they can pick it up themselves if they want, or better just get a keen weapon), but I do like the idea of improving the crit multiplier. This also helps emphasize the synergy between the Swashbuckler and Duelist (my prestige swashbuckler linked earlier has a increase to crit threat range as its capstone).

I was however thinking, as another way to up damage, would it be out of line to add on the bonus from the Paizo swashbuckler? Say instead of the power attack Penetrating Strike, you get Precise Strike upgraded to be xd6+duelist level bonus to damage.

Other possible option: Go the 4e route and make Precision damage dice maximize on a crit. On a crit with a x3 multiplier, maximize and roll 50% of the dice (round up), and on a crit with a x4 multiplier maximize plus roll the normal dice.

So say you have your 2d6 sneak attack + 5d6 precise strike, you crit with a rapier, instead of 7d6 (average 24.5 damage), you just add 42 damage. Adding on the increased multiplier to make it x3, you instead get 42+4d6 damage (average 56), and if you have a x4 multiplier, you get 42+7d6 (average 66.5 damage). This makes precise strike more potent, and emphasizes crits as a major damage dealer.