I don't revisit this one and haven't since the 1990s in any recurring way, nor have I seen it since the obligatory blu-ray purchase because it's dated fairly badly in too many scenes. It's a time capsule of a movie, which may not have been its intent but is the best way to view it.
Having said that, I might give it a viewing this weekend and see how my perception of it has changed - if at all or again or anywhere in the middle. Maybe after I watch "Major League" again...
What I liked about the movie:
* The fish-out-of-water trope works as the crew are now outside their natural environment, tripping over themselves and not in a belittling way. This is the nice lighthearted schmaltz needed after 2 serious movies, since TOS mixed up serious and light fare between episodes as well. The jokes that still work are terrific.
* The punk on the bus scene
* the punk music that everyone on the bus hated
* At the time, the movie appealed to general moviegoers as well as fans. Nobody knew fully what to expect when the movie showed on the screen and it struck a chord for casual moviegoers, which helped to make TNG a success.
* How the crew are properly serious in their own timeline, before and after their escapade, which adds a sense of balance and ensured audiences would want to see what would happen in a next film. (Though I still miss "Tomorrow is Yesterday" - the only time travel story that doesn't ha-ha-bonk it up every few seconds, this isn't "Airplane!".)
* Intentionally scripted as such or not, all humans except for the one token loner who are the nutjobs. It's a nice twist to all of those movies that say loners are bad eeeeeeeeeeeeeevil people. (But they one thing they all have in common is this: They're just movies)
* Luckily for Kirk and the gang, they meet the perfect loner working in the perfect place
* The effects when the Probe arrives at Earth were pretty good if not fantastic overall
* It's one of the more popular 80s Trek internationally:
https://www.the-numbers.com/movie/Star-Trek-IV-The-Voyage-Home (sales were 2.5x that of III, and 1.5x II)
What I didn't care for:
* Riding off the wild success of the previous two films, they could have done anything and it'd still rake in enough viewers for a sequel.
* People who clamored to see this in 1986, if shown the same movie today, will they perceive it just as highly as they (probably) had back then?
* Why not get the Excelsior? With transwarp, that would make the galactic journey in STV almost plausible instead of feeling like a throwback to VI. (True, TNG didn't have transwarp either and it never once galaxy-hopped...) That, and Just how many Constitution Class ships do they keep in the refrigerator to pull out every time they get the munchies?
* The "let's use edited highlights of the previous film" token bit makes even less sense, nor should a fan sit there and think "Let's see: Klingons were doing a home video recording of the Enterprise being blown up and we'll ship the video in MP374 format to the Federation because it'll help our case, whatever that is, and because it's a galactic video compression format."
* Out of time or not, the only reason they would send CHEKOV to the Noocwear Wessels (and not made by the Widdle Owd Wady een Wenningwad) is to be the butt of several stupid jokes and/or to try to prevent their own mission from succeeding. But it leads to the only moment of real tension in the movie (as well as a couple good jokes by Dr McCoy as well as pill poppin' to fully save a pair of kidneys in
minutes), so it's not all bad.
* The same movie tells us a complete tally early on, then 100 minutes later undercuts it... by three charges, if memory serves.
* At the time, non-nerd kids were slagging the movie before its release upon hearing rumors that time travel would be involved and saying the TARDIS and/or Christopher Lloyd would be involved
* Of all the Kirk era movies, even KelvinKirk, STIV has the least amount of plot depth. That's saying something when Kelvin movies enrich us with "magic blood" as a panacea for a grossly contrived flop of a scene...
* the incidental music was a bit too light, it kept me thinking "Wow, a couple small rewrites and this could be a Brady Bunch movie". The power of music, indeed... Anyone been to Hamelin lately to check in on the kids?
* Who's the target audience in this movie and what were the ratings of such targeted demographics? Not too many people I know of are illegally poaching whales - either for breakfast, to keep Bender Robot lubricated, or anything else and I suspect the vast majority of domestic audiences weren't.
*Fish-out-of-water could only work in this movie. Having them trip over themselves as the butt of jokes in all subsequent films in their regular time and place just makes them all look like rear parts of donkeys. (even NuSpock and NuUhura in their daytime soap bickerings, but the Kelvin movies, especially the first one, are just substance-less nostalgia squeezin's anyway.) ST IV set the stage for comedy and it doesn't make a bit of difference if 2 or 2 Trillion people watched and/or enjoyed and/or hated it, the fact remains subsequent movies all tried the ha-ha routing in a belief it can just be applied like butter on a muffin. Especially if the muffin was made without the yeast and eggs to counterbalance but everyone looks at the recipe and determines the outcome of tasting it differently.