Revealing mistake: When they are learning how to throw knives, the guy gets one thrown through his hand. If you watch this carefully, blood starts coming out of his hand before the knife hits. (00:28:45)
Revealing mistake: When Rico jumps on to the back of the tanker alien and starts shooting at its back, you can see the outline on the back of the tanker that is going to be shot up before Rico starts shooting.
Revealing mistake: During the last play of the football game, Dizzy throws Rico the ball and he does an impressive flying flip over several players. Right before the flip, it's extremely obvious that Rico runs up an off camera ramp/stairway in order to perform this flip.
Revealing mistake: Just before Dizzy gets skewered by a warrior bug, you can see breakaway panels on her body armor at the points where the CGI bug impales her, to cover the squibs used to make the holes. The shot is already shown in slow-mo so it's easy to spot.
Answer: The card face up is the one he's trying to guess. The card that flips over is his guess (you can see him hit a pad when he says "ace of spades".) So he is trying to use mental powers to guess the card that is face up (which he can't see as he has his back to it), and (presumably so the computer can track his results better) he makes his choice on a keypad, which then turns over the card on the screen (which is why the card is what he said, yet still wrong).
Gary O'Reilly