Mike goes to a check cashing place with a personal check for $10,000 from his professor. Check cashing businesses never cash personal checks on the same day; they require a 3-5 day waiting period so the check can clear. And even if it was a payroll check, the business would have taken a percentage to cash it, so Mike would not have had the full $10,000 to bring to the game.
The filmmakers have stated (in interview with ESPN.com's Bill Simmons) that the cash checking location is run by a friend of his professor's, but the scene was cut to bring the film's running time down.
In the first game between Mike and Teddy, Teddy flashes his Aces as if it were the guaranteed winner and gets up and leaves. He never sees Mike's cards. Mike could have had pocket nines for 4-of-kind to win.
When Worm approaches Mike at the Taj Mahal poker room and sits down the dealer is "washing" the deck. (Placing all the cards face down and mixing them up before shuffling.) As the camera goes from behind Worm to behind the dealer, the cards go from "washing" to shuffling as the camera angles change.
When Worm and Mike go over to Grama's place, Worm is chewing a cocktail stick the whole time which he throws away when he begins to yell at Grama. Grama promptly grabs him by the collar and the cocktail stick is back in his mouth again.
When Mike and Worm visit Grama together, Grama lists the amount owed as $25,000. This was the original amount owed, but he already took the first $10K back from Worm. Later in the same scene, Grama goes back to demanding the correct $15K amount.
In the first part of the final poker game between KGB and Mike, when KGB has just reraised $5000, Mike starts pushing all his chips forward to go all in, the shot is taken from behind KGB and you can see KGB's left hand touching his face. The next shot from the opposite direction (when you see the continuation of Mike pushing his chips forward) KGB's hand is down on the table.
In the first hand of the last game, Teddy was playing dealer and had had the big blind out while Mike had the small blind out and acted first. In a heads up match, the dealer is the small blind and is the first to act.
Mike enters the Troopers card game wearing a jacket, is thrown out of the game without it, and is shown later wearing the jacket again. But you can (barely) hear the jacket get thrown onto the ground after him.
When Worm is waiting for Mike outside Mike's apartment, stickers on the window say "NO ENUS" with both words centered. "ENUS" should have been shifted to the right, as the original word "MENUS" would probably have been centered when the letters were originally applied.