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Continuity: When Johnny is about to download the data he puts on some kind of headset held in place with an elastic band around the back of his head. The next shot is a close up of him plugging a wire into the datajack on the back of his head. The elastic band is nowhere to be seen even though the next shot shows that the wire is nearly touching it.
Continuity: When J-Bone is coming down from Heaven, the lift he's on stops quite a way off the ground, and moves when he steps off it. Yet when he, Johnny and Jade step onto the lift, it seems to be on the ground as it doesn't move. It couldn't have been lowered, as we would've heard the noise of the motors.
Revealing: In the beginning when Keanu Reeves goes to a ruined building in the ghetto to get the info inside his head extracted (at least that's what he expects) he comes across a couple of bad guys. Watch closely though as he hits the black guy, and you'll see that he actually doesn't hit him at all.