When Jack is dealing poker at his friends house party, after an elaborate shuffle he offers the cards to be cut to the gentleman on his left, if he were a professional he would know that you cut to the right and deal to the left.
When Jack removes his shirt at Bella's place, we see the wound on his left shoulder across the collarbone. Later on when he removes his shirt in front of Jani at Giles's house, the wound is further down on his chest.
When Jack is taken off the roulette table approx 20 minutes in, the roulette wheel is not spinning. Roulette wheels are only stopped when the table is closed, and as there are players at the table the wheel should be moving.
When Jack has a job interview at the London casino his father recommends him for, the manager (Mr. Reynolds) at one stage asks him the current count at the Blackjack table. Jack insists it is -9, the manager insists it is -8 to which Jack confides smugly to himself "It had taken him 45 minutes but Jack now had Mr. Reynolds number. The man couldn't count."
Neither Jack or Mr. Reynolds can count. The count is actually at +2.
During the interview scene, the manager (Mr. Reynolds) at one point asks Jack for 1800 in 25s. He proceeds to incorrectly give him 68 chips, which at 25 value only amount to 1700. He should have actually given 72 chips.