Revealing mistakes: In different takes the "Wall-Street" numbers on the display panel are the same, the numbers never really change and it is more or less always the same stocks, no matter what time it is.
Factual errors: The long string of digits representing pi in the opening of the movie is incorrect starting in the ninth decimal place.
Factual errors: The logic followed by the Kabbalists with respect to Hebrew numerology is flawed. First, there are no zeroes in the Hebrew numerological system. Second, in Hebrew numerology, the different letters have values that vary in the number of digits (the values range from 1 to 400, with only the first 9 letters having single-digit values.) Therefore, it is impossible to create a specific 216-letter-word in Hebrew given a 216-digit-number with zeroes in it. It has been argued that the Kabbalists do not use Hebrew numbers to decipher the code, rather, they use the modern western number system to correlate the 216 character name to each Hebrew letter. Nevertheless, the premise seems to be muddled, at best, if not completely flawed.
Incorrectly regarded as goofs: When Max is in the coffee shop, the cream container he opens has a McDonald's logo. It's a cheesy enough place that they were probably ripped off.
Factual errors: When Robeson is discussing Archimedes' Principle with Max, he states the definition of density as weight per volume. Density actually refers to mass per volume. Any scientist or mathematician would not mistakenly say weight, as weight is an unpopular measurement among them.
Continuity: The note suddenly appears on the Go board between shots when Max enters Sal's living room.
Factual errors: Max mentions that the Golden Mean is represented by the Greek letter theta. In fact, it is phi or tau.
Factual errors: Max writes the golden ratio as (a/b) = (a/a+b). It should be a/b = (a+b)/a, if, by definition, a>b.
Factual errors: When Lenny demonstrates basic examples of Hebrew numeric coincidences, he gets the numbers right but mistranslates some of the Hebrew. "Kedem" does not mean "Garden of Eden" but is a biblical word means "East" (as in "East of Eden"). Also, "Etz Hakhaim" is not the tree of knowledge but rather the other tree in the garden, the tree of life.
Factual errors: Max' ticker displays some stock prices in thirds, but real stock prices only used halves, quarters, eights, sixteenths, and so on.
Crew or equipment visible: Shadow of camera operator visible looming over Max as he thrashes on the floor of his bathroom.
Continuity: When Max is examining the sticky ant remains with his fingers, the substance switches from being on his middle finger to being on his index finger in the close-up.
Continuity: The number on the screen just before Max faints and is revived by his neighbours shows 218 digits, not 216.
Factual errors: Max suggests that the Kabbalists have already tried all possible 216-digit numbers. That is 10 to the power of 216 - if they had been doing a quadrillion a day since the destruction of the Temple, they would barely have begun.
Incorrectly regarded as goofs: Max shaves his head and draws a square around the bulge on the side of his head. Later on, when Max is chasing a photographer from the subway, there is no square on his head. This could be due to time shifts in the story, and hallucinations had by Max. Making the actual linear time of events impossible to tell for sure.
Errors made by characters (possibly deliberate errors by the filmmakers): Max indicates that he medicates himself with "Promazine 'HCI'." The proper name of the drug is "Promazine HCl," where the HCl stands for hydrogen chloride. The error likely occurred when either Max or a filmmaker mistook a lowercase "L" for a capital "I" on a bottle or prescription.
Miscellaneous: When Max sees ABR stock price in the newspaper in the subway, it is 6 1/2 but net change from previous day is +2, a large increase, as opposed to a big drop. It was predicted by Euclides that ABR will fall to 6 1/2 after trading above 40 for years, so net change should have been -35 or something.
Factual errors: Max tells the Caballists that they've probably written down every 216 digit number. He must know this is impossible. Millions of supercomputers working since the Big Bang couldn't make a dent in writing down all the possibilities.
Factual errors: In the opening credits, Pi is written as 3.14159265263124534. But the value of Pi is actually 3.1415926535897932384.
Errors made by characters (possibly deliberate errors by the filmmakers): In the scene where Lenny Meyer saves Max from the Stock Market people, there is a brief shot of Farroukh swinging the baseball bat at them. This is because originally Farroukh, or at least Faroukh and Lenny together, was supposed to save Max.