When Jane is given the $100 to play blackjack, it's in cash. The very next shot shows him playing with casino chips, but then in the next one he gives the cash to the dealer to get chips.
During the scene in the casino where Matt Etienne says, "Yes, and we're really wondering what your secret is," one can see his hand on Jane's right shoulder. But when Jane says, "There's no secret, I'm memorizing the cards," it goes to another angle and his hand isn't on his right shoulder anymore.
When Patrick is playing blackjack at the low stakes table, the dealer uses a "shoe" which holds multiple decks of cards. But when he moves to the high stakes table with a minimum of $1,000 per bet, the dealer is dealing cards directly from her hands. No properly-run casino would allow this inconsistently. If anything, the casino would reserve the shoe for the high stakes tables only to avoid the very fraud that Patrick identified.
Organ transplants are covered by insurance.
When Jane is examining the severed hand, the bones are arranged one on top of the other. A real hand will have the bones side by side.
When Jane is explaining his Memory Palace to the squad at the restaurant, and is telling Grace what Cho and Rigsby have in their hands, he asks Grace to shuffle the pack and draw a card. She shuffles and then draws the Ace of Spades, but she should have burned that card before she drew it.