During the opening credits, while Ben is riding his bike on the road, you see the same orange PT cruiser go past twice and the same silver Chrysler 300C go past three times.
When Ben's mom is serving birthday cake to Ben and his friends, she serves Cam twice.
In the first Las Vegas casino scene, the team enters the Hard Rock but the closeups of Ben's $500 chips show "red rock" on their labels. The Red Rock casino scenes occur much later in the movie.
The first night the group gambles in Las Vegas they are in the Hard Rock Casino, however the table at which Ben gambles says "Red Rock Casino". When he switches tables it says "Hard Rock Casino."
During the chase at the end of the movie Jill alternates between running in heels and running barefoot.
AT the tailor shop where Ben works, he mental-calculated the total price for the couple with various discounts : belt $49.95 (15%) jacket $589.99 (10%) pants $285.99 (10%) shirts $69.99 (5%) shoes $155 which should come up to $1052.33. However Ben's sum was $1042.68 which is incorrect.
In the beginning of the film, Ben receives a promotion in his job at the menswear store, and a raise to $8 an hour. In Massachusetts in 2008 the minimum wage was (and still is) $8.25 for retail workers.
Jill says that she is "comped" a suite at the hard rock hotel, however as a counter/spotter she should only be making minimum bets, which wouldn't be enough to get a free suite out of a Vegas Hotel.
In the MIT grading scale for undergraduates, GPA is out of 5.0. On numerous occasions throughout the movie, it is stated that Ben has a 4.0. On the MIT scale, this would be a "B" average.
The method mentioned as the Newton method is in fact called the Newton-Raphson method because Raphson's contribution is well established (i.e. not something that would be impressive for a student to know) and in fact, the way Raphson approached it was simpler and is the one featured in books today despite the fact it bears both names. It's also well known that Newton developed his method first even though he didn't publish it for quite some time after Raphson published as was Newton's modus operandi. The Newton-Raphson method is also quite basic and is covered in most high school curricula around the world ergo not something that merits a lengthy conversation in class, particularly in MIT.
When Miles shows Ben the source code of the robot, Ben looks at them and immediately says this is very good. Actually, even a highly experienced programmer could not understand a source code just by looking at it for 2 seconds, especially the code of a really complex system such as this robot.
All the cards in the casino scenes have rounded corners opposite the index numbers, identifying them as used cards that have since been removed from use on the casino floor and altered so they can never be sneaked back into play.
When Ben leaves the Hard Rock Hotel after their first night in Vegas, the shadow of the Cameraman and Camera on the dolly are visible on the hotel front and security guards in the background.
There are multiple errors in Vegas hotel locations - seeming to be in one hotel when the shot from the window makes it clear they are elsewhere, particularly when visiting a suite said to be at the Hard Rock but clearly the view is from a tall Strip hotel. The Hard Rock Hotel is neither.
The outside shot of Ben's dorm building is the Towers dorm for Boston University. Ben would not be living there as an MIT student.
Why didn't Ben keep his winnings in a safe deposit box? He can add more whenever he wants and it would be safe from everybody, particularly Micky.
When Micky knows Cole Williams is pursuing him, why did he continue to go Las Vegas to win money and count cards? The amount of money that can be won, the casino rules of Black Jack and the mathematics of card counting are the same in other casinos located in Atlantic City, Reno, and other casinos located throughout America.
The notion you require an exceptional mind to count cards is faulty. Any person of average intelligence can gain proficiency in even the very sophisticated systems with sufficient practice however the method used in the film, "Hi-Lo" counting is the most basic system that can be learned very quickly by anyone.
When Ben is first shown losing, he is assumed to be at a table because of a beneficial count. When he begins to lose, Kianna signals to leave the table by running her fingers through her hair. However, the cards dealt were low cards, which would be increasing the count to be more beneficial. Ben should stay at the table according to strategy, as the count during that specific hand just increased by 2.
For some unexplained reason, Ben, Mickey and the rest of the MIT group limit their repeated cheating antics to the same casino, where they were bound to eventually come to the attention of casino security. It would have made more sense to never visit the same casino more than once or twice.
When Ben is in the casino playing for the first time, the count is +18. We then see a face card (worth 10) appear and Ben wins. Mickey then asks him what the count is. He says +18, but it's really +17 because a face card has a value of -1.
During the first trip to Vegas, when they're grabbing their fake IDs off of the bar, the IDs are laminated. When the camera angle changes to the team looking at their IDs are plastic cards with a magnetic strip on the back.