Continuity mistake: When Wynn looks at Rains' file, the drawer her file is in is slightly open before he finds it. The shot cuts to Dodd reading the paper, then back to Wynn, and her drawer is shut. (00:32:40)
Visible crew/equipment: When Rains wakes up she stands up and shouts "Where is she? What have you done with her?" you can see the camera's shadow moving on her. (00:18:10)
Visible crew/equipment: In the beginning when the man comes climbing down the ladder you can see a tape marker on the floor. When it cuts it's gone. (00:01:10)
Revealing mistake: When the man is melting after being covered in acid in the beginning, you can see a wire pulling the "melted skin" off his arm, at the bottom of the frame briefly. (00:04:00)
Continuity mistake: When Rains spits on Haskell shortly after meeting him, you can see the spit trailing downwards. In the next shot, however, it inexplicably lands on Haskell's cheek, who's a good foot taller than Rains.
Continuity mistake: After Ryjkin is doused in acid, he begins to bleed on his shirt, partially obscuring his name that's stitched into the shirt. A few shots later, as he starts to pull his face off, the name is completely free of blood.
Continuity mistake: When Wynn enters the elevator, location arrow points to direction 1 o'clock between down and up. Elevator starts to lower, but now initial position of arrow has changed nearer to up position, to 2 o'clock. (00:45:55)
Continuity mistake: When Meyerhold throws the boots into the ice room, you can see it spinning, and there is absolutely no shoelace trailing off it, yet he somehow manages to pull a shoelace from the now broken shoe.
Plot hole: When the fat guy throws a boot into the ice-spray room, it freezes and shatters on the ground. You can see the length of the shoelace on the ground as well. The shot cuts to the guy in the shaft, and he pulls up the shoelace to reveal the end encased in ice, while the end is halfway into the ice block. This wouldn't be possible, because the other end of the shoelace had no ice at all, and there's no sign either of it breaking.
Answer: No, the director himself has stated they're not the same person, however they wanted to show that Kazan wasn't always like that, he went through the same lobotomy that Wynn did It also, when viewed in that aspect, gives a much darker perspective to the ending of cube 1 when you realise that the "white room" was NOT an auxiliary exit, but rather one just like the room from Cube: Zero where the "god" question would be asked.