I've really taken a liking to Joker and have played him the most of any of the cast. TBH, I really like his trait design, in theory the character is one of the most well put together designs in a long time. His design is all about confusing and frustrating your opponent into doing bad things, and that's exactly what the joker would want from his opponent.
The parry is the icing on the cake. The Joker is much like Makoto is SF4, her offense is so frustrating that people just press buttons desperate for a way out. I've learned how to parry KF slide on wakeup after setup, avoid grundy throws with low parry, etc. His strings are all pretty safe and let you parry your opponents wakeups pretty easy, it just takes some conditioning. Really, I only have small issues with his trait and propose the following changes:
HAs are permanent throughout the round. LBSH, no one at top level is going to consistently get 3 HAs in a round, and even if they did, that last one would come mighty late in the match.
Improve the speed per level of HA. It seems like only 3 HAs are worth a damn, levels 1 and 2 are barely noticeable, this should be improved or evened out across all levels of HA.
Let teeth combo off of parry! This is the most important one! Teeth pop people out of throw attempts but not out of parry, this is dumb. If I put teeth on you on wakeup, you try to to wakeup with a special and I parry it, under those specific conditions, I should be rewarded with a combo off teeth.