After Jake has gone bust at the poker tables, Holt produces another stack of cash, which he explains is his own money that he withdrew from one of the 25 ATMs in the casino. Banks have a fairly low limit on daily ATM withdrawals, usually between $300-500. The limit is per day, not per trip to the ATM, so there being 25 ATMs available would be of no further help in acquiring the money. He would never be able to withdraw that much cash.
While undercover in the casino, Jake exchanges $15,000 in cash for chips at a poker table. Legitimate casinos have cashiers at the entrance to exchange chips. It is never done at the tables.
Captain Holt wears his Commendation breast bar above his World Trade Center Breast Bar. When the WTC bar is worn, it is worn above all other medals, but below the American Flag bar.
To prove he has no feeling in his leg, Scully stabs himself in the thigh with a pencil. His hand bounces slightly and shifts off to the side, clearly not penetrating the skin, yet a stabbing sound is heard and when he lifts the pencil again there is blood on the tip.
Scully stabs himself in the leg with a pencil, drawing blood, yet there is no hole in his pants.
When Rosa has a butt cramp, she drinks from a bottle of blue sports drink and the cramp instantly goes away. Not only is that not how cramps work, but the bottle is still completely full after she drinks from it, despite several loud gulps being audible while she is drinking.
When Captain Holt goes on a gambling binge, he admits to betting on "something called the NLCS." Major League Baseball's National League Championship Series normally occurs in mid-October, and this episode is set sometime after the annual Halloween episode, making it too late for the NLCS to still be in progress.
Holt is discovered by one of Valdano's men because the 9-9 crew neglected to check for "poopers" in the bathroom before discussing their mission and Holt's gambling problem. If the man were actually in there pooping, the odor would have alerted the detectives, even if the man could have stayed perfectly quiet while they were talking (which he wouldn't have had much of a reason to do, as he'd have no reason to presume anyone entering the bathroom wouldn't be a fellow casino patron).
Amy is not wearing her proposal ring.
Although not an official tournament, there are several violations of poker etiquette during Peralta's game, such as chips being stacked in slots underneath players' arms; or the dealer's vocal commentary on which hand wins (any experienced player would immediately recognize full house as the winning hand).
Captain Holt mispronounces "acai."