While Picard and Riker talk to Data at the science station at the start of the episode, you can see a static star field above them from the dome, while they are traveling at warp speed.
Seconds before entering the Holodeck, Scotty's hair is neatly combed and parted to one side. Moments later, when the camera angle changes as he is entering the room, his hair is mussed in front.
In the opening sequence, Picard and Riker are standing behind Data, who is seated at Science Station 1. After encountering the Dyson Sphere's "turbulence", both men turn and begin walking towards the center of the bridge; Data is seen rising from his seat. In the next shot, Picard and Riker come down the ramp and approach the Ops station from the rear, but Data is shown already seated there and operating the console.
As Scotty walks to his station on the original Enterprise bridge, the stopper in his bottle can be clearly seen. When he pours his drink to toast the absent crew, the stopper has disappeared.
Seconds before Scotty enters the Holodeck he is completely drunk -stumbling, slurred speech. When Picard joins him in the holodeck he appears sober. That whisky was real alcohol, not synthehol. He should be drunk throughout the entire scene.
We can see curvature as the Enterprise approaches the Dyson sphere. Given the theoretical size of a Dyson sphere (roughly the size of Earth's orbit around the sun), any curvature of the sphere while the Enterprise was that close would be imperceptible.
Dr Crusher informs Scotty that he has "a hairline fracture of the humerus" - the bone of the upper arm - while she's very carefully scanning his lower arm.
When Scotty first learns that Riker and LaForge are from the Enterprise, he says: "I'll bet it was Jim Kirk himself who hauled the old girl out of mothballs to come looking for me." This would've been impossible for Scotty to say. This episode takes place after the events aboard the Enterprise B in Star Trek Generations. At the time of this episode, Scotty thinks Kirk is dead. However, it is not unreasonable for Scotty to be somewhat confused after being suspended for 75 years in a transporter. He may need a few hours to regain his full mental capabilities.
It is odd that Picard doesn't mention to Scotty that he recently went on a mission with Spock and arranged to have them reunited. But why would he? Spock was currently involved in a highly classified mission on Romulus, and its doubtful Picard would mention this in informal conversation with Scotty or anyone else. And there is no reason to suppose Spock, a Vulcan with little need for sentimentality or nostalgia, would choose to "catch up with old shipmates".
It was established early in the series that Data is an android and- as such- is unable to use contractions in his speech; yet- when making his report to Captain Picard & Commander Riker about the Dyson Sphere- he says "we've been unable to find any signs of current habitation" instead of "we have". However, Data is constantly striving to become more human and may have learned such linguistic behavior from those around him.
Data states that the interior surface of the sphere would have the equivalent area of 250 million class M planets. M class planets are identified by the habitability of their atmospheres, not their size. However, at this time in Star Trek history, M-class planets were actually classified by their comparibility to Earth, which would suggest a similar gravity and size.
Scotty, a stocky man and regular drinker, becomes roaring drunk from only a couple of drinks (the bottle is still nearly full when he goes to the holodeck). However, we do not know if it's the same bottle or a second one. Or what his tolerance to this particular drink is.
Scott has a hairline fracture of the humerus, which is the long bone in the upper arm. Despite the fact that the arm is probably still tender and sore, Geordi bumps Scott's arm several times while walking down a corridor, and at one time, he grabs it while Scott has no reaction. Then, while Scott describes what happened on the Jenolen, he gestures with that arm, feeling no pain at all.
In the remastered version, it can be seen that the Jenolan is labeled Jenolin. (See trivia.)
Captain Scott and Commander La Forge are having a casual conversation just after beaming up to the Enterprise while en route to Sickbay. They enter the turbo lift on deck 12 which doesn't make sense as Sickbay is located on deck 12.
The second time Geordi taps his combadge, it chirps before his hand makes contact with it.
When Scotty asks the Computer to load the program containing the main bridge of the Enterprise, the Computer tells him that there have been five ships under that name and to provide an exact registry number, to which Scotty says "NCC 1701" without any suffixes. The computer then immediately loads the program containing the main bridge of the Enterprise from the Star Trek (1966), however the Computer did not take into account that there were technically two versions of the NCC-1701 Enterprise; the original Constitution-class model (from the TV series), and the refitted model (from the TOS movies). Additionally, there were variations for both across the series and movies. The Computer should have asked Scotty to specify if he wanted the bridge of the original Enterprise or the refitted version.
When shown to the shuttlebay, Scotty blurts out to the assembled command crew that they are giving him one of their shuttles. No one had mentioned giving him a shuttle. It's a very strange conclusion to come to simply based on their presence in the shuttlebay.
The entire command crew of the Enterprise assembles in the shuttlebay to see Scotty off, even Worf, with whom Scotty did not seem to get along. That would have left a junior officer in command of the ship for no great reason. As third officer, Worf could have easily been left out of the gathering and taken the conn until a higher-ranked officer returned to the bridge.
The diameter of the sphere is said to be comparable to Earth's orbit around our sun. Assuming the star in the sphere is a comparable size to the sun, it would take years if not centuries for the Enterprise D to approach its photosphere at the speed the tractor beams are shown to have pulled it. If the star were large enough to be that close, the sphere could never have been built, and it would be molten.
When the bridge crew of the Enterprise is attempting to turn the ship into orbit around the star, Data announces that they have turned "right." The proper navigational term would be "starboard," not "right."
After re-materializing, Scotty thinks that he has only been missing a short while, yet makes no note of the fact that Riker, La Forge, and Worf wear a style of uniform with which he'd be completely unfamiliar.