Visible crew/equipment: In the very beginning of the movie, Ben is seen riding his bike over the bridge in an aerial shot. Near the top of the screen, if you look carefully at the end of the bridge you can see a police barricade at the end of the bridge. It is there because the bridge is closed for filming.
Continuity mistake: During the scene in which Ben is introduced to the card-counting group, several members are sitting at a blackjack table. There are cards on the table in front of them. In the first shot, the cards are face up, in the next, they are face down, then they appear face up again. While no one is seen or heard dealing cards, the number of cards on the table changes in several shots.
Factual error: Jill tells Ben that she has a suite at the Hard Rock and asks if he would like to see it. In the next scene it shows her looking out the window (presumably at the Hard Rock) and seeing the fountains of the Bellagio. This is not possible as these two resorts are almost two miles apart on different roads.
Continuity mistake: The subway scenes between Jill and Ben show someone in a coat with black and white squares get on the train. However, a later scene shot throughout the subway car's window shows this same person wearing the same type of coat sitting down on a bench with a friend at the subway station as the train pulls away.
Visible crew/equipment: At the bar where the 21st birthday is being celebrated, you will see the microphone/boom come into the shot from the top of the screen. This happens while the "mom" is passing out the cut pieces of cake. It has a bright colored wind screen on it.
Other mistake: In the opening scene, Ben is seen riding his bike over the Mass Ave Bridge from Boston towards Cambridge, at MIT. A few moments later, he is seen coming over another bridge (the John Weeks footbridge) from Boston into Cambridge, at Harvard. There would be no reason for him to ride into Cambridge over the Charles River at MIT and then seconds later be riding into Cambridge over the Charles River at Harvard.
Plot hole: After Ben loses the money and he and Mickey get into a fight, Ben talks the rest of the MIT players to risk their own money and take all of the reward instead of giving 50% of the take to Mickey. Kianna says they need at least 100 grand to play - where did they get this money from? The movie leads you to believe that Ben lost all of Mickey's money on their first night there, so they have no winnings with them. Ben's money is back in his dorm room, and you could assume the rest of them don't all have bank accounts with cash sitting in them for IRS reasons.
Revealing mistake: When Jill gives Ben the money after the first night, you can see it is just a $100 bill wrapped around a bunch of $1 dollar bills.