When Nick starts playing, Roxy tells him that her shift is off in 10 minutes at midnight. New dealer comes in and Nick keeps on winning. When he goes back to bet all the winnings for the last time, Roxy is again dealing at the table. She should not be dealing as her shift was over.
When Nick is at the diner listening to Mr. Casanova, the waitress brings him a full glass of ice. As Nick squeezes two grapefruit halves into the glass, the ice level changes. After squeezing the grapefruit juice into the glass, Nick goes to drink from a large glass full of juice with some ice at the top of the glass. It would take the squeezing of many grapefruits to fill a glass that size.
Nick suggests to his customer inside the Golden Gate Casino, to take a taxi cab to the Caesars Palace, which would only take 1 minute. Since the Golden Gate is on Fremont Street and Caesars is on the Strip Center, a taxi would need more close to 20 minutes, depending on traffic.
When Nick goes to speak with Danny DeMarco in his suite at the Golden Nugget, you can see the Las Vegas Strip (the Eiffel Tower stands out...) outside the window. The Golden Nugget is on Fremont Street downtown, NOT on The Strip.
When Holly is dumped outside the hospital, it is in actuality West Jeff Medical Center in Marrero, LA, just outside New Orleans. That's a long way from Las Vegas, NV where the film is set.