In the staff meeting, Picard says the next time he visits the holodeck he'll invite the ship's historian, Whalen. Later, in his log entry, he refers to Whalen as a fiction expert. That's hardly synonymous with historian.
The detective is punched near the temple. He falls down, but then holds his jaw.
Geordi and Wesley claim that the crew members in the holodeck could vanish if the computer problem isn't solved correctly, but this isn't true. The holodeck is simply a place where holograms are projected and can have physical effects upon humans if the safety protocols are removed. The only harm that could come to the people trapped in the holodeck would be something that happened to them in the program, such as being shot or falling. If the holodeck program were taken offline, the crew members would simply be left in a bare room, which has been shown in numerous episodes.
Since everything created on the holodeck is unable to exist outside the room, when the captain is kissed by the lady in Dixon Hill's office the lipstick on his cheek should not remain once he leaves the holodeck.
However, it has previously been shown that the holodeck also replicates some materials, as when Wesley is still wet after leaving the holodeck, in 'Encounter at Farpoint'.
When Data is in the holodeck, the tone of his voice changes to that of a stereotypical 1930s/'40s street character from that era. It makes sense that Data would begin to use the vernacular of the hard-boiled detective genre, as he has read the complete stories of Dixon Hill, but he did not view any movies, so how would he know how these characters would have talked? (He's the only one who speaks like this; even holodeck characters don't sound as ridiculous as Data.) However, as he had read the entirety of the Dixon Hill novels, he would have also noted any described speech patterns mentioned in the novels.
The secondary plot involves Picard studying to deliver a greeting in the convoluted language of an alien species; the opening scene has him suffering through a practice session. But since he has access to the universal translator, and since the language seems to contain the same phonemes as English, why wouldn't he simply have Data or a linguistics specialist program the greeting and the language's rules into the computer, and let the computer render it phonetically?
However, it has been established elsewhere that, with some languages and races, the speech rendered by the Universal Translator can be recognised as automatic translations. This why Uhura was forced to use archaic paper copies of a Klingon dictionary in Star Trek VI. Making the effort to speak another race's language might be seen as a courtesy.
When Picard tells Data to "Try the exit in the hall." it would seem to indicate this particular holodeck has, or has the ability to generate, a second exit, unlike what will be shown to be the case with other holodecks in the future on numerous occasions throughout the series.
Data uses the words "he's" and "I'd" in the Holodeck in spite of the oft-repeated claim that he cannot use contractions. This may be due to his adoption of the vernacular of the 1940's gangster scenario.
When Redblock and Leech step out of the holodeck, Leech gets a worried look and stares down at his feet well before the "fading away" visual effect begins.
When Data tips his hat in the final scene, the palm of his hand has no makeup.
Data enters his quarters and requests information from the computer regarding the Dixon Hill novels. He is only seen in closeup, but based upon the unique overhead lights and the curvature of the computer console in front of him, this scene was clearly filmed on the bridge set.
On the holodeck, Mrs. Bradley kisses Picard. When Picard leaves the holodeck, he has a lipstick stain on his mouth. If everything in the holodeck consists of holograms, the lipstick should have disappeared as soon as Picard left the holodeck.
When Wesley attempts to fix the holodeck and the surroundings switch from Dixon Hill's office to a snow storm and back, the actors are all in slightly different positions.
When Picard first enters the holodeck, the computer asks for all manner of time period and location data and then asks for a file or access code. All that location and period data should be stored in the file anyway. A well-designed user interface would put that query first since it could obviate the need for any follow-up inputs. (This is done in order to give some exposition about the upcoming holodeck program, of course.)
When Dr. Crusher is at the police station, a molded plastic bottle sits on the water cooler. In 1941, water bottles were all glass.
When Picard, Data, and Lt. Bell open the doors to the running holodeck program, a "modern" police siren is heard. In the 1930s, sirens were mechanical, and sounded nothing like what was heard.
When Leech points the gun at Dr. Crusher, it is heard being cocked, yet when the entire gun is seen the hammer is not cocked.
When Picard is in Dixon Hill's office, he hears a car horn blow. He walks to the window in a long shot and pulls down the blinds. They make a crinkle sound as a metal blind would. Then we see a deep focus shot of the street through the pulled-down blinds. The close-up of Picard's hands show him holding down flat wooden blinds. Wood blinds make no sound when bent, unless they break.
Dixon Hill's office is supposedly located at 350 Powell Street in San Francisco, yet when he looks out the window, there is a flat street with a building on the other side. 350 Powell Street is on a hill, and it overlooks Union Square, a park that takes up an entire block. Also, since San Francisco's famous cable cars run on Powell right in front of this address, there should be a gap in the street for where the cable cars' "grippers" attach to the cable. Finally, we should be able to hear the sound the underground cable makes; while it is running, it is very loud.
Once the crew members realize that the safety protocols are not functional, Data should immediately use his superhuman speed and strength to disable all the armed men. Even if he were shot with the small-caliber 1941 weapons, he would not suffer any major damage.
The whole episode revolves around the trouble with opening the holodeck doors to rescue the Captain and crew when the system malfunctions. At no time, however, is the alternative of using the transporter to beam them out, and then fixing the systems when no-one is in danger, proposed.
Since Data is capable of duplicating other people's voices, it would have been easy for him to duplicate Picard's and memorize the Jaradan greeting in a fraction of the time Picard spent studying for it, with the Jaradans none the wiser. For some reason, this option is never discussed.
When Dr. Crusher enters the holodeck, it appears that she will be indoors, possibly Dixon Hill's office. The scene changes to the police station and Dr. Crusher comes in. There is no explanation given as to how she would know to go there to find the captain and the others.
The crew keeps referring to *the* holodeck. But in the pilot, it was mentioned that there were 16 holodecks.
Cyrus Redblock is unfamiliar with the word "computer," but he should know it, especially if he is a business man, whether legal or otherwise. In the 1930s and '40s, the word "computers" referred to people whose job was to do complex mathematics, especially in the fields of accounting and engineering. It was, in fact, the job that was eliminated by the invention of electronic computers, beginning in the late 1940s.
Picard, at one point, has trouble describing a city block to his crew, but city blocks make frequent appearances in 24th century Earth in this and other Trek series. There is no reason Picard should have had trouble describing something so common.
When left in command of the Enterprise, Riker still sits in the first officer's chair. Whoever is in command of a vessel, even temporarily, is entitled to, and indeed should, sit in the captain's chair.
When Beverly asks for more light while treating Whalen, Data carries a lamp towards her. In doing so, the plug for the lamp is pulled from the wall socket and the lamp turns off. Data is mystified by this development, but seems pleased when (unseen by him) Picard plugs the lamp into a socket nearer to Beverly and the lamp turns back on. As Data learned about 20th century Earth in preparation for this program in the same fashion Picard did (reading the Dixon Hill novels), and Data has perfect memory, he should be just as aware as Picard, if not more so, how the lamp functions.
Cyrus Redblock purports to have manners, yet his first instinct when "Dixon Hill" won't cooperate is to kill "the woman." By a 1940s sense of chivalry, men were not to harm women. Even if one assumes that Redblock is simply feigning his etiquette, to keep up appearances, he should have behaved as etiquette and chivalry demanded and threatened Beverly last, not first.