The whole Teleporter Accident scene. Other than Rule of Drama and a chance to show off the new transporter FX (which would be changed in subsequent movies) the whole scene seemed illogical. If they were rushing to get the Enterprise ready to go, and the transporters were acting up, why not just use a transporter on Earth or a space station to beam people over to the ship? The whole point of the transporters is that only one side of the transport needs to be the pad (and this restriction would later be eliminated). In theory, another transporter could beam people to anywhere on the ship. Kirk's new officers could have literally been beamed directly to the bridge to report in! After all, it's not like Starfleet wouldn't have exact coordinates for something parked inside their own space dock.
How did the story originally end?
Since this story began life as a pilot for a new Star Trek series, and Decker and Ilia were to survive the pilot and stay on as regulars in the series, How would the Phase 2 version of V'Ger been told (in Dr McCoy's words from ST 4) what to go do with itself?
To elaborate a bit if you don't want to follow the link, Kirk proves that humans are the creator by repairing V'Ger's burned-out relay and V'Ger then goes off exploring further. There is no "joining with the creator". Ilia was being held captive rather than absorbed and is released.
Twenty Minutes into the Future - Robert Wise creates the first vertical video
Am I the only one who finds the one shot just after launch that is shot from the ceiling directly down on the Navigation Station and Captain's chair to be somewhat jarring? Of course this would be more a Horizontal Video than a Vertical Video (For those not knowing the term, it apples to people you tubing videoes on hand held devices vertically instead of horizontally.)
It may have been a Call Back to the first shot of the first TOS pilot, which tracks through the bridge dome from above, showing us the bridge crew busy at their stations for the very first time. It was a really awkward shot that didn't look good in The Cage, so (and this is total speculation on my part) I wouldn't be surprised if the shot was included in the movie because it was finally practical to film it the way Gene or someone else on the production staff had always wanted it to look.
The Motion Picture Has No Fashion Sense
What in the bleeding hell are those black things on the crewmembers' tunics supposed to be in ST:TMP? I've never even seen any behind-the-scenes info on what function they're supposed to serve, and they look like they'd be hideously uncomfortable.
The belt buckles? They're supposed to be "Perscan" medical monitoring devices. But you're right about the uniforms being uncomfortable, George Takei stated that because of the way it was designed it required assistance to be removed even for minor things such as using the restroom. The redesigned uniform featured in the rest of the films with the original series cast was brought about because of the cast's reluctance to film any further films with this version of the uniform.
Worse than that, William Shatner said it was extremely painful for the male castmembers to even sit down in them. Basically the first film was a lot more dreary and militaristic and the uniforms were supposed to reflect that. Instead they just reflected what a miserable time everyone had making that movie.
So....why did she have to take an oath of celibacy? The only explanation I remember being given in the movie was that she wouldn't take advantage of a "sexually immature" (whatever THAT means) species.
Deltans are a very sensual race. Anything That Moves doesn't even being to cover it. Apparently sex for them is both extremely culturally significant and also transmit telepathic information between the members involved, sending anything from speech to memories or pain relief. However, with a human or other species is dangerous because 1. the Deltan may demand for more sex than the human can supply, and 2. the telepathy may go bad for your brain. Much of that had to be cut out of the film because, well, G rating.
Short version: someone had a fetish for sexually supercharged bald women but they couldn't show the former trait in a general audiences movie.
Thruster Suits & the Deadliest Son of a Bitch in Space
Spock's thruster suit was really pretty cool. This Starfleet-issued EVA garment comes with a big thruster on the back that lets the wearer travel short distances at relatively high speeds. You can even jettison the thruster once it expends its fuel. I've go to ask, though does Spock's suit have any sort of reaction control system? I'm working off memory, but I don't recall ever seeing evidence of one. How the heck do you maneuver or even come to a stop without one once you've discarded the main thruster pack?
The fella floating outside Epsilon 9 is seen to use small thrusters on his suit. Though they only seem to appear on the back and don't seem very powerful.
Spock's thruster suit was designed as a one-time-use engine to escape from an area when other means weren't feasible. It appears that his suit didn't have any RCS thrusters on it, but it is highly illogical to believe that Spock would go on a fact finding mission and have no way of relaying those facts back to the ship.
They Took Away His Parking Space, Too
Other than further emasculating Decker and codifying the Decker Family motto: Stay the hell away from Jim Kirk, was there any universe-consistent reason to demote him to commander? We've seen flag officers command starships in TOS, and by Star Trek V: The Final Frontier the Enterprise has no fewer than three crew members who hold the rank of captain (Kirk, Spock, and Scotty), so why not just let everyone keep their rank for the duration of the mission?
Out of Universe reason: In The Original Series one of the staples was the Insane Admiral or Obstructive Bureaucrat who would step in and ruin the Captains life as he tried to command his ship in the face of their interference and they didn't want Kirk to come off like that (although it does give a nice inversion to the Kirk-Decker dynamic from "The Doomsday Machine" with the roles reversed and now it is the younger Decker with the older, higher ranking and obsessed Kirk). The In-Universe reason is that it is simply how Starfleet prefers to do it in that era, possibly as a reaction to all those TOS Admiral/Captain conflicts so it ensures a clean chain of command and they later changed it.
Wait, so our brave Captain Decker suddenly has his ship seized by the backroom wranglings of an Admiral who has been long since Kicked Upstairs, and this Admiral proceeds to declare himself Captain and demote Decker before arguing with him about every major decision? Are we sure this isn't just the stock Insane Admiral plot, plus one Perspective Flip?
That's probably a valid interpretation—at least for the first half of the film. The movie goes to great lengths to show that Decker really should be the one in command. And really, until Enterprise intercepts V'Ger, Kirk hardly seems like the same man from the series. In fact, TOS!Kirk probably would have called TMP!Kirk out on his crap almost immediately. It isn't until they make contact with V'Ger that Kirk starts making the right calls and acting like the James T. Kirkwe know.
Where is that external view coming from?
This happens twice. Starfleet manages to hack into the sensor net of a Klingon battlecruiser attacking V'Ger, which shows the cloud destroying another battlecruiser, before finally showing the cloud destroy the viewpoint battlecruiser with some sort of electrical discharge... which continues to record several seconds after the entire battlecruiser, including the presumed installed external camera, has been destroyed.
The poor Starfleet sensor array gets the same treatment when it is attacked. The Enterprise gets uninterrupted footage of the cloud when it destroys the sensor array, and the camera mounting it.
The array, at least, may have had some sort of satellite instillation nearby that had the 23rd century equivalent of a camera pointed at the station. Maybe a transmitter, or something, that had to be set some distance away from the main facility—something autonomous enough to continue recording and transmitting its telemetry to Starfleet Command after the main array is destroyed.
Notice how those cameras just keep on recording just fine even as they are supposedly being destroyed themselves? They must put more redundant circuits in the cameras and transmitters than in the whole rest of the station.
Why make up a new probe?
Why did the filmmakers create an entirely-fictional Voyager 6 when using the real-world Voyager 2 would have worked as well? There were only 2 Voyager probes ever planned, so "Maybe they thought there would be more?" wouldn't work.
Perhaps simply to establish Star Trek as having an Alternate History vs the real world. An interpretation that is basically canon now that the Eugenics Wars have failed to materialize and lead to World War III on time.
They might have hoped that the higher numbered probe would imply more advanced technology, specifically much faster propulsion systems. The probe was stated to have fallen through a black hole, but currently the closest known black hole to Earth is V4641 Sgr, which is about 1600 light years away. Based on my, admittedly shaky mathnote Seriously, I'm terrible at math, so if I'm wrong, someone smarter than me is encouraged to correct this,, it would take over 2.43779×1019 years (that's more than 24 quintillion years) for one of the real-world Voyager probes to actually get there—and that's assuming a constant velocity for the entire trip, which is impossible. To get around this problem, the probe would have to have an FTL drive of some kind. Maybe a series of much more advanced future probes were called 'Voyager' as a legacy name to honor the original Voyager program; much like the series of progressively more advanced Federation starships are given the name Enterprise.