The big problem with the stick in the MK1/MK2 (it affects both, since they're the same stick) .. is the swing time from one side to the other. If you are pressing right to run to the right in Sonic and want to stop suddenly, you'd slam Left. But the time it takes to get left makes your stop sluggish, and you'll probably hit whatever you were trying to avoid. It makes reflexive twitch movements to dodge attacks extremely difficult in shooters, it makes playing special stages in the Sonic games making sharp turns nearly impossible, as the turns are 90-degree and require split second reflexive response.
This doesn't harm all games, especially those that benefit from wide sweeping 360-degree rotations, circular moving or shooting motions, like Ecco the Dolphin, Gunstar Heroes, or Contra to name just a few. But the numebr of games it makes pleasant to play pales in comparison to the number it makes unspeakably aggravating to play. It feels, to me, like I am moving an 8-direction lightswitch. There's an ON and an OFF on each end, and in the middle it just doesn't do anything. It goes beyond deadzone and into a territory where it practically needs its own name.
Inaccuracy is somewhat improved with the MK2, since the old orientation biased the stick towards diagnols and now, it is biased towards the ordinals like any decent control method. (Suffice to say this is an improvement for just about everything, unless you played an awful lot of Sonic 3D Blast or other heavily diagnol-movement oriented games.) Things like suddenly pressing Down to get into a pipe in Mario while running over it, or going into a door by pressing Up in SMB2 will likely still prove as much a challenge as they were, with much frustrating walking left and right instead of going through the door.
There are a lot of faults in the GP2X that are really forgivable once you get into running some really fun software on it. But a faulty stick hinders the whole experience and is something I cannot possibly overlook.