Goofs

Picard requested that the turbolift take him Deck 9, crew quarters, but his quarters are on Deck 8.

When Ensign Gomez accidentally spills hot chocolate on Captain Picard, initially she hardly spills any liquid on his uniform (most of the hot chocolate appears to spill on the floor and on her). Yet, later, as Picard is walking down the hallway to the turbolift and encounters Q, almost the entire front of his uniform is soaked. There was not enough liquid spilled on him to make such a stain. We also see a larger stain on Gomez's uniform as Picard leaves and she turns toward Geordi.

When the first Borg beams onto the Enterprise, Q begins describing it to Picard as neither a he or she, but then refers to the Borg as he and him.

In previous episodes, any time someone transports onto the Enterprise without warning, the ship's intruder alert is triggered almost instantaneously. However when the Borg scout transports into Engineering from the Borg cube, the intruder alert is not triggered, and his presence goes unnoticed until Geordi spots him and calls for ship's security.

As Guinan warns Picard to protect the Enterprise from the Borg, Picard orders the shields raised. Moments later, even though the shields are active, the Borg beam over. Considering that they are technologically much more advanced, it is conceivable that they may have found a way to transport through shields.

After the Borg take the Enterprise's shields down with their shield-draining weapon, they fire one more time. Once again, it appears to hit the shields around the Enterprise, even though they're supposed to be down. The fact that this shot disabled the warp engines with no damage to the ship, indicates that those "shields" were actually the warp field. Numerous appearances of warp fields throughout the series show that they do have roughly the same ellipsoid shape as the shields. Although normally a warp field isn't supposed to glow under fire like the shields do, the Borg torpedo, unlike other energy weapons, was obviously designed to impact the warp field, thus creating a similar glowing effect.

Riker, Worf and Data decided to board the Borg Cube. Riker told Guinan this, as he was leaving the conference room, but she advised against it. His premise was that it's only fair we return the favour after the Borg boarded the Enterprise. The next scene shows Riker, Worf and Data in the transporter room ready to be beamed across. O'Brien tells them he has set in coordinates to set them down in the least damaged part of the Borg Cube. He wasn't at any of the meetings with the other crew discussing the situation about the Borg and none of the crew, including all the senior crew, had never encountered the Borg before, never mind what they were called. How could O'Brien possibly know to refer to them as the Borg? Only Guinan was aware of their existence and when she told the senior crew in the conference room what they are called, the name was new to them. It doesn't seem feasible he would know this.

However, the away team would not have turned up to the transporter room without briefing the transporter chief about what was happening and where they were going.

When Picard enters the turbolift after Gomez spilled her hot chocolate on him, the Turbolift doors indicate that he is on Deck 10, while the doors immediately to the right denote his correct location of Deck 36.

When Picard enters the bridge to address the situation with the Borg tractor beam, there is a small, lightly-colored place marker on the bridge carpet to show him where to stand.

After Q hurls the Enterprise to system J-25, Picard orders all stop, and Wesley confirms the order was carried out. However, before Q makes his "the hall is rented" speech, the stars are seen to be moving behind him, meaning the Enterprise was still moving.

When Guinan seems to touch a panel to bring up the image of the Borg Cube on the screen in her office, she never actually touches it, but the screen comes on anyway.

When Picard has hot chocolate spilled on him, he doesn't show any pain from the hot liquid.

While Picard and several others are meeting in the briefing room, Worf calls from the bridge to announce that the Borg have locked onto the Enterprise with a tractor beam. The Borg cube is visible on the viewer in the conference room, yet no tractor beam is seen. A subsequent exterior shot shows a bright green tractor beam connecting from the Borg ship to the Enterprise.

A second Borg appears, to take over from the one Worf phasered. Just before it bends over the body of its companion, a tear can be seen in the neck area of the skullcap covering the actor's head and neck.

Toward the end of the episode after Q leaves the bridge, you hear Picard say engage but his mouth doesn't move.

Geordi questions whether food should be eaten around the engineering controls, but there is a food dispenser in the middle of the room. Also, the controls are sealed shut.

For some reason, Picard feels the need to have Guinan walk to her office to view the Borg ship when she's able to see it just fine from the windows of Ten Forward.

Data says that the damage done to a planet is identical to the destruction of the Federation outposts in The Neutral Zone (1988), implying that the Borg were responsible. This means that the Borg already know about the Federation, which seems to contradict Guinan's warning that the Borg will attack, now that they know about the Federation. Even if the outposts were too small to get the interest of the Borg, the Borg would have likely assimilated the people living at the outpost and thus their knowledge. Even if they didn't, the outposts would have contained hints that they were part of a much larger and highly advanced civilization. Because the Borg attacked both Romulan and Federation outposts, they would also have learned that they were dealing with two separate cultures on less than friendly terms with each other.

Once the crew realize that Picard is not on the ship, Riker orders the ship to stop and they begin a search from that location. It would make more sense to find out exactly when Picard left the ship, return to where they were at that time and begin the search there.

After the Borg have 'carved the ship like a roast', and that section's being pulled towards the Borg cube, look almost dead-centre between the two beams (the green tractor beam, and the white beam pulling the section towards the Borg cube); there's the back-end section (almost an entire half) of an automobile embedded into the cube. Borg ships are supposed to be very large, compared with Enterprise, but, no car (it looks to be the back end of a Porche - possibly a Delorean) has ever been built that large.

After Q kidnaps Picard, Picard reminds Q that he agreed to leave his ship alone. In Hide and Q (1987), the agreement was that Q would leave humanity alone, not just the Enterprise.

While trapped on the shuttle with Q, Picard states that, even if Q keeps him there or he dies there, "the Enterprise will continue with Riker as captain." It is highly unlikely that Starfleet would allow the young and relatively inexperienced William Riker to remain in command of the fleet's flagship on a permanent basis. Indeed, several years later, Picard leaves the Enterprise for a covert mission and another captain, Edward Jellico, is given command of the ship in case the mission went south and Picard did not return.

After Worf identifies the 6th planet of the J-25 system as Class M, Data says, "There's a series of roads on this planet, which indicates a highly industrialized civilization." Data is not supposed to be able to use contractions.