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.
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.
When Ben is riding his bike on the bridge, a young guy with a lady are passing in the back stage. After this, when a yellow stripped bus passed behind Ben, that young guy and lady disappeared (it seems, they jumped into water) then another lady in white jacket appears who was absent before in the back stage.
When Ben meets with Mickey and the group for the first time, he explains the basic rules of 21 and deals himself a face-up card, then the camera cuts to Ben then back to Mickey and now Mickey's card is face down.
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.
In the montage scene showing the "extravagant" lifestyle of the group, the film cuts to scenes at the blackjack table, inside of clubs, etc. It's supposed to happen in or around the Planet Hollywood Casino/Hotel, but many of the locations shown are from Red Rock Casino game room and the club "Cherry". Red Rock is about 12.5 miles northwest of the Strip, surrounded by houses and deserts.
Later in the movie Jill tells Ben the Hard Rock has comped her a suite and asks him if he would like to see it. In the next scene they are in a suite over looking the Bellagio fountains. The Hard Rock is not on the Strip and does not have that view to the Bellagio fountains. The suite is more likely to be in the Planet Hollywood (the old Aladdin) or even Paris.
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.
In the shot of Ben counting cards on the first arrival in Vegas, Ben's tray-table is down. If the plane is as close to arriving as the view from the window shows, tray-tables must be in the "up and locked" position.
In two separate places in the film, the player is hollering for the dealer to draw a "monkey" (a face card or a ten) when, in fact, a monkey would have given the dealer a winning hand. The first instance is when an Asian woman introduces Ben to the slang. The more egregious of the two instances is when Ben (who, by this point, has established his big player credentials) calls out for a monkey twice when either of those times would have given the dealer a winning hand.
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.
The goof item below may give away important plot points.
A key clue that makes Cole Williams suspect Ben of being a card counter is that Ben did not double down on 11 when the count was "cool". Basic blackjack strategy dictates always doubling down on 11 (because the odds of making 21 are very high - even casual players know this). The only situation where it would make sense not to double down is if the count was very negative (lots of low cards in the deck). But as the "big player" in the MIT system, Ben would have left the table long before the count became negative.