Continuity mistake: 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 mistake: 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.
Spider: Get on the table.
Johnny Mnemonic: Why?
Spider: Don't be a bigger asshole than you have to, get on the table.