Goofs

Data plays blackjack. The dealer deals him a 7 and a 5 in the wide shot; however, in the closeup, the cards become a 3 and 2, thus allowing Data to get the Five-Card Charlie. (Though the odds are slimmer, a Five-Card Charlie can be achieved with a total of 12 on the first two cards.)

When first playing blackjack, the dealer's card changes from a queen of clubs to a king of diamonds. When Data comes back to ask questions after being in the hotel room, the dealer's card is also a king of diamonds. Obviously the shots somehow overlapped resulting in the first blackjack scene's cards changes.

When viewing the revolving door from the outside, Worf enters first, Data second, then Riker misses the third section and enters using the fourth section of the door. When viewing the revolving door from the inside of the casino, Worf enters first, Data second, and Riker enters immediately after Data, rather than using the fourth section of the door. (This may have since been "fixed," as Riker is not shown entering the door.)

The elevator in the lobby of the Royale is a sliding telescopic door, with two panels. When the away-team first enters it to go upstairs, it opens fully; that is, both panels pull to the right and into the internal mechanism of the elevator. However, when Worf and Data (together) and Riker (alone) come back down, the elevator doors only open the first panel, just enough for the passengers to disembark.

When Data first rolls the dice while playing craps, one die almost stops before making it to the other side. This can be seen based on how he threw them. In the next shot, the dice are seen hitting the end of the table, giving him 6.

Early on, Geordi states that the surface temperature of the planet is -291°C. This is physically impossible as the minimum temperature possible in the universe is 0 K (-273.15°C)

While Data "cuts" the deck of cards at the Blackjack table with the entire deck in his hand, the bottom cards of both sides can be seen. They are both the Queen of Spades.

When Commander Riker leaves the elevator in the Hotel Royale by himself, the door quickly opens and immediately closes after he steps out. Since the story of The Hotel Royale takes place in the 20th century, there are no hotel elevators whose doors would open and close so quickly.

After beaming the Charybdis' shard aboard, Riker and O'Brien immediately pick it up, with no ill effects. The metal should still be as cold as space (-270 °C; -454 °F), which would freeze the skin off of their bare fingers. However, the transporter may have automatic features to warm up objects to safe temperatures.

At the craps table where the away-team is playing, there are numerous errors in standard casino procedure, such as the way the stick man holds the croupier stick and the way chips are placed on the pass line and don't pass line.

However, this could be attributed to the fact that the aliens based the Royale microcosm on a poorly written novel, and the book probably does not list the specific procedures.

Multiple errors during Data's blackjack game: 1) Texas tells Data to "Ante up." However, one does not ante in blackjack, one simply places a bet. 2) The players are holding their cards in their hands. Players are not permitted to touch the cards at all in casino blackjack. This is to prevent card tampering, either accidental or on purpose. 3) The dealer has Data cut the deck, which violates the rule about players touching the cards. 4) There is only one deck of cards being used. Casinos use multiple decks for blackjack. This gives the house a slight edge in the game, and helps to make card counting more difficult.

While this is true for Blackjack played in casinos on Earth, the casino in The Hotel Royale is based on aliens' interpretation of the content of a badly written novel. It is doubtful the book contained detailed rules on the casino games.

Two errors with the play at the Blackjack table (with Vanessa, Texas, and Data): 1) When playing Blackjack in casinos, the players are *never* allowed to touch the cards. The dealer is the one to shuffle and deal the cards exclusively. Data wouldn't be allowed to shuffle. 2) Related to #1: since the players can't touch the cards, their hands' cards are dealt face-up; also because there is no need for secrecy. Only the dealer's first card is face down; this creates the speculative nature of whether to hit or stand to beat him. His hidden card is only revealed after everyone has finished hitting or standing.

While all of this is true today, back in the mid-20th century, the setting for this casino, players were allowed to touch the cards, and the cards were dealt face-down.

When Riker, Data, and Worf attempt to leave the hotel (unsuccessfully) through the revolving door, the actors are very clearly just walking in a circle. There are no alien shenanigans.

In the hotel, Worf is unfamiliar with the twentieth century elevators and finds he has to push a button to call for it. However, later on, the twentieth century telephone in the hotel room rings, and Worf seems comfortable answering it.

The camera crew can be seen in a mirror on the craps table.

Riker, Data, and Worf take some time to grasp the nature of the simulated Royale world, even though it is the same principle as their ship's Holodeck.

When the woman calls the hotel room and asks if the officers want room service, the three of them are unfamiliar with the concept. Data guesses that she is asking if they want the room cleaned. The aliens who created the simulation of the hotel based their knowledge entirely on the novel aboard the astronauts' ship, so that is how they knew what room service was. As Data had read the entire novel in a previous scene, he, too, should have known the term.

When Vanessa shows her hand to Data, he suggests that "the odds favor standing pat" with a total of thirteen when the dealer is showing a face card; in fact, drawing a card is the mathematically correct play, though by a slim margin.

Pierre de Fermat died in 1665. That would make it about 700 years, not 800, until Picard's time.

Near the beginning, when Picard is talking to Riker about Fermat's Last Theorem, he says "When Pierre de Fermat died, they found this equation scrawled in the margin of his notes." This is not quite correct; he actually wrote in the margin of a copy of "Arithmetica", an ancient Greek text by the mathematician Diophantus, and what Fermat wrote was not the theorem itself (which was already contained, without a proof, in the text) but the fact that he had discovered a remarkable proof which he didn't have room - he claimed - to write in the margin.

Riker notes that, since the flag patch on Colonel Richey's uniform has fifty-two stars, it "places it between 2033 and 2079 A.D.", which is in the 21st century. However, when requesting information about the colonel, he states that they are in a 20th century structure and that Colonel Richey is from the same era.

Riker states that the 52-star flag patch "places it between 2033 and 2079 A.D." A.D. stands for "anno Domini", which translates as "year of the Lord". A.D. is properly placed in front of the year number, not behind. Many people make this mistake in real life.