Continuity mistake: The Bird of Prey is the one captured by Kirk's crew in ST III. That ship's bridge showed Klingon Cmdr Kruge in his elevated command chair with his helmsmen arrayed circularly below him, and nothing else. ST IV has this same ship; however, the bridge now resembles The Enterprise layout with Kirk's command chair behind Sulu and Chekov at their rectangular helm, with Spock, Scotty, and Uhura at their usual positions.
Suggested correction: According to the captain's log at the beginning, they have been on Vulcan for 3 months. As they prepare to depart, we see several Vulcan technicians moving equipment in and around the ship. It's quite conceivable that the bridge was reconfigured according to the crew's specifications to facilitate their use of the ship. This may seem a bit excessive, as the remodel includes the door onto the bridge, and the frame of the door, and possibly most of the rest of the ship. But it's not outside the realm of possibility. The real mistake, though, is why they would go to the effort of installing new workstations on the Klingon bridge and marking them with Klingon labels, instead of standard Federation text. Interestingly, though, the "Starfleet" style bridge layout of the Klingon ship is being used by the Klingons on the Bird of Prey in Star Trek V.
Other mistake: During the inquiry at the start of the movie, the Klingon Ambassador is going over the footage of the destruction of the Enterprise from all the exterior views. This is very nice, but how would they have access to all of these different viewpoints of the destruction? Bearing in mind no-one was there to film it. It couldn't have been the Klingon Bird of Prey that filmed it, because in most of the destruction scenes, the Bird of Prey would have been no-where near or in a position to film it, and was of course captured and still being commanded by Kirk during the course of the inquiry. (00:04:10)
Suggested correction: Most of the visuals we see on view screens in Star Trek are created from sensors rather than cameras, so what we see doesn't necessarily have to be from the visual perspective of the ship taking it. Though yes, it is quite an amusing coincidence that it all looks exactly like they're watching a copy of Star Trek III on home video.
Suggested correction: It's possible the Grissom and/or the Bird of Prey launched drones into orbit to aid in the scanning of the planet or for communications or sensor relays, and this is where the footage could have come from. This isn't unlike the beginning of Star Trek: The Motion Picture, in which crewmembers of the space station mentioned such drones as the reason images of the aftermath of the V'ger destruction were able to be seen despite no ships being left.
