Continuity mistake: Before Max's computer blows up, it predicts that a specific share will fall over 30 points. The next day, Max is on a subway train and borrows a newspaper from another passenger so he can check the stock prices. The price of the share indeed has fallen, but the text next to it indicated it has risen two and a half points, rather than fallen by over thirty.
Continuity mistake: As the whole story is so much focused on the mysterious 216 digit number, you might find this one especially amusing: When the computer puts out the number for the second time (the first time the number is not fully visible), switch to freeze frame and take a close look at the display: the number has actually 218 digits.
Continuity mistake: When Max Cohen writes down the 216 digit number when his printer fails to work, he looks at the number he wrote down later; it is a different number. (00:54:30 - 00:56:15)