I'm sure it will be beat, but here's a first stab at it with 137 characters. It doesn't do any fancy screen control to keep it all on the same line, which some movie versions probably would.

Consider it 125 characters if you don't want to see the random code for reference. As a middle ground, how about 128 for seeing the original on every line?

I've always wondered how many people notice that it's smarter to check the whole passcode as a unit than to be able to short circuit each character match. I guess the tension doesn't quite build the same when the WOPR just keeps failing as when the camera shows it getting closer, though. Joshua even had the advantage of scrolling all the digits simultaneously and locking each in separately from those before it in the code. At least they made the end of the world base 36.

Update: added spoiler tags

Update 2008-09-12, 18:27 UTC:
How about 122 for seeing the original on every line and 119 for never seeing it?