The movie's premise makes time travel in the Star Trek universe seem much too easy. We can only assume that that ship was special because it belonged to Christopher Lloyd.
Maybe, but it wasn't without precedent in the series — this was actually the third or fourth time they'd used that method of time travel. Plus it did have its limits, in that it caused huge stress to the ship that was attempting it, and the range was apparently limited to a few centuries in either direction.
Fourth, actually. They did it three times in TOS. Twice on purpose.
The movie does indicate that relatively small miscalculations could have bad effects in timewarp. They risk it here because, well, it is the only plan they manage to come up with.
The dream state is what effectively acts as the ultimate limiter. It only lasts a matter of minutes if you hop back a century or two, but beyond that you could spend days, weeks, or months just laying there asleep.
Time travel in Star Trek IS easy. It's just generally a bad idea.
The time cops in DS9 's "Trials and Tribble-lations" groaned upon hearing that James Kirk was involved with Sisko's story, calling Kirk a 'menace' and was responsible for 17 separate time violations.
I think everyone's taking this one too literally. If he could get a DeLorean up to 88 MPH, of course he could get a Bird of Prey to travel through time.
Those prior time trips were taken on the Enterprise, not on a Bird-of-Prey like on this trip. Maybe the Enterprise is just better suited for time-travel. (Judging by what Scotty says about "these Klingon crystals" being drained by the trip, Federation dilithium crystals may be inherently superior.)
The line "Damage control is easy. Reading Klingon, that's hard!" is actually a in-joke. The original foundations of the Klingon and Vulcan languages stem from the first Star Trek film. And were actually put together by...James Doohan (Scotty).
When the rest of the crew are splashing around celebrating in San Francisco Bay after the Probe departs, Spock is very noticeably not enjoying himself. He tries to climb as high up on the Bird of Prey's hull as he can, resists the efforts of the others to drag him into the water with them, and lets out a growl of disgust when they finally succeed and he surfaces. On one hand it's funny because Spock is usually The Stoic, and you'd expect him to be reserved and dignified. But then you remember Spock is from Vulcan. Vulcan is a highly-volcanic Single-Biome Planet that's almost entirely covered by mountains and deserts, with only a few small scattered seas. He doesn't like the water because he's from a planet where thanks to modern irrigation technology one could go their entire life and never see open bodies of water. Spock diving into George and Gracie's tank earlier was merely done out of necessity.
The crew all know San Francisco well because they went to Starfleet Academy there, yet Chekov and Uhura have no idea where Alameda is. Alameda was probably either bombed into oblivion during one of Earth's major wars, or sunk due to sea level rise.
While it's great and all that the Planet is saved at the end, eventually, they're going to have to repeat this mission. At best, a humpback can live about a hundred years; if George and Gracie's kid lives that long, the humpback will go back to extinction around Picard's time.
Keep in mind that people in the 24th century seem to have mastered cloning.
The novelization explains that there are samples of humpback whale DNA preserved on Earth, but that without a pre-existing whale to teach the clones how to act like humpback whales, there would be no point. Presumably these samples are used to boost the population to a self-sustaining level.
The whales are also completely alone, with no others of its species. However, according to the Novelization, whales have always had good relations with other marine mammals like dolphins.
While there may be no other Humpback whales left for George and Gracie to talk to, there are a great many other species of baleen whales, many of which are far more numerous than humpbacks (though none of them sound as nice when they burp at each other). They would likely have had plenty of company to talk to.
If we accept that hump-backed whales are endangered and every single one of them (especially "very pregnant" ones) matter to the survival of the species, then it's quite possible that by taking two away, as well as an expert / activist (who now, without a job, had plenty of time on her hands to work on behalf of the whales), that it's possible Kirk may have inadvertently caused their extinction! Yes I know they were being hunted at the end, but we don't know whether they would have escaped from the whalers...
Would two whales + one baby + one human expert make that much difference though, compared to the dozens/hundreds of whales being slaughtered every year despite efforts to the contrary?
Not to mention the ecological catastrophe(s) of the coming decades in the Trek 'verse; the Eugenics Wars-WWIII.
Imagine being a pilot in one of those little shuttles that you see flying around inside Spacedock as the Probe passes by. Not only are you stuck in a powerless metal box with dwindling air reserves, it's only a matter of time before you collide with part of Spacedock, another shuttle, a starship...
Assuming Gillian's boss is basically not a bad guy, just a bureaucrat doing the best he can who felt forced to screw over her whale project because he's under a lot of pressure...imagine how he feels after the movie's events. He deals Gillian a severe professional and emotional blow, tries lamely to apologize; Gillian (understandably) slaps him, calls him a son of a bitch, and is never heard from again. From his perspective, she presumably either went to live off the grid in some connected-with-the-sea remote island community, or has thrown herself off a cliff.