The presence of the T-1000 is a departure from the story given in the original film. Reese explicitly stated that the Tech-Com had won in 2029, defeating Skynet and capturing its time displacement center. The first T-800 was sent back in time literally at the last minute as a desperate measure on Skynet's part; nothing on this narrative hinted that Skynet still had time to send a T-1000 following back (or that something like the T-1000 existed in the first place). And even if it did, Connor and company could have potentially altered the plan to save Sarah from the first T-800 by sending Reese and the reprogrammed T-800 to the same period. It has been fan-wanked for decades that the events in Terminator altered the main timeline and created a different John Connor and a different Skynet instead of forming a Stable Time Loop (that is, that there was a first John Connor whose father was someone from his time instead of a time-traveling Reese), therefore altering too the circumstances of the 2029 victory, but nothing has ever been said officially about it.
The T-800 states that his human part has at least a minor form of Healing Factor, and he accordingly acts as if he could regenerate anything with enough time given, as indicated by him nonchalantly sacrificing the flesh of an entire hand only to convince Dyson of his true nature. In the previous film, the first T-800 didn't demonstrate this ability: his human part effectively died due to comparatively smaller battle damage and started literally rotting away, which forced him to don a weak disguise in order not to immediately give it away that he was a cyber-zombie now.
The previous film had established dogs can sense the true nature of Terminator and go mad everytime one approaches. In this film, Enrique's dog doesn't even bat an eye in front of the T-800, and no explanation is given about why. (Unlike a similar point in Dark Fate, however, this Ass Pull is sufficiently small to be considered more of a production goof.)
The films outright negates T2's established rule about fate and predestination, showing that, even after blowing Cyberdyne up and melting the reprogrammed T-800, another Skynet rose anyways due to the Air Force buying Cyberdyne's patents, only in 2004 instead of 1997 and in a software form ironically much more difficult to defeat (and indeed, unlike the previous film, this Skynet had apparently not been even defeated by the time an Arnold was sent to the past). It's inevitable that fans see this not only as a mean-spirited copout on the previous films, but also as a gratuitous excuse to repeat the plot of T2.
The novelization of the film contains another by revealing shockingly (a subplot actually filmed but deleted from the movie) that the Air Force had already started projecting the Terminator line and that the T-800's face comes from a Sgt. William Candy from 2004. This could only work if this Skynet and the one from the original duology were one and the same, which they are not, as they were created at different points from different timelines; in the first one, there were no Terminator project before the 1997 Judgement Day, and Arnie's appearance came presumably from a random person from the batches of humans Skynet was using to experiment on. That said human happened to be that timeline's version of William Candy would turn it into a wild Contrived Coincidence, especially because in T3 Candy was apparently a Deep Southerner who happened to be sent to California specifically for the project.
Given the extensive rewriting and reshoots the film suffered, it's little wonder that the final act feels disjointed, in particular the revelation that Skynet had been using Marcus all the time to find and lure John. Prior to that, there was zero indication that Marcus was not simply an escaped experimental subject: in the climax, the machines grant him access to the Skynet base because they recognize him as a pawn of Skynet's plan, but up to that point, all the machines Marcus had found since waking up had been regularly attacking him with clear intention to destroy (including the Harvester Transport that kidnapped Reese, which should have had strict orders not to kill Marcus given that Kyle was part of the same plan). Skynet's Serena Kogan interface even implies that finding Kyle was also part of Marcus' mission, which makes even less sense having in account that their encounter happened actually by sheer luck.
The human resistance now having apparently resources to spare, with all of its members being healthy, well fed, with clearly high morale, and equipped with matching futuristic armors. Flashbacks from the first film showed that their ray guns (which were probably scavenged from destroyed machines) were the only fancy thing about them: their fighters were visibly emaciated, wearing dirty rags and looking like pauper Vietnam vets in their own time. While Salvation justified its own change with the events of T3 resulting in part of the American military infraestructure being saved, there's no similar justification in Genisys.
The film's breaking point is the T-5000, whose presence in the future changed all the timelines. However, he comes officially from an "unknown alternate timeline", eschewing any explanation of what event could have possibly generated a scenario where Skynet developed a nanotechnological-infecting Terminator incarnation for itself and reached the main timeline to change things up (particularly given that he also seems to know exactly the events of the main timeline, as the second T-1000 shows), if that actually explains all the Timey-Wimey Ball. Similarly, who or what sent Pops to the past is never explained. Those mysteries might have been meant to be solved in the two sequels that were in the works before being flattened by Genesis's box office failure, but there's not a hint that could make one guess how, unless it was by throwing at least one more Ass Pull to the mix.
The concept of the time points allowing people to share memories with their versions of other timelines. This had never been mentioned in any of the previous films, and sounds more like Science Fantasy than the relatively grounded approach to time travel used in the original duology.
The fact that the T-1000 now can repair disabled Terminators with a mere drop of polyalloy is seen by some as breaking the character's fundamental nature, as it had been explicitly said in T2 that it could not utilize its mass for anything more complicated than forming a blade. An argument in favor of it is that the repair probably wasn't more than creating a wire to reroute power, but this is still more complicated than the aforementioned.
The T-1000 suddenly has the ability to leave pieces of itself behind to act as a tracking beacon for its targetsan ability that would have come in handy a few times in T2. In older materials, it was even stated that doing this was impossible for the T-1000 because it could only track its components up to a few dozen meters, and Skynet specifically programmed it to prioritize maintaining full mass because even losing small pieces over time would gradually make the creature less effective.
Franchise wide, this film contains a change that nullifies the entire premise of Terminator: an extra T-1000 was sent from Connor's time to 1974, altering all the timeline, yet absolutely nothing changed in their own time as a consequence of this, with Reese only finding about it when he reached the past. The film even shows onscreen that the T-5000 is now reigning supreme in 2029 after having massacred the resistance when Kyle was gone, making explicit that the multiple changes in the past neither changed nor erased his timeline. According to this, had the first T-800 or the T-1000 managed to kill John, nothing would have happened to the time plane where the humans had defeated Skynet, which the T-3000 then confirms himself by openly stating he can freely eliminate John and Sarah without affecting his own existence.
Pops's T-800 CPU having the probably incredibly complex software and hardware needed to control the polyalloy and enable him to return as a half-T-X is jarring to many people, with the given explanation that "all the alloy needed was a CPU" being seen as cheap and flimsy.
The idea of Skynet sending multiple Terminators to the past directly contradicts both the original film and T2, where the first T-800 and the T-1000 were essentially Skynet's last resort to kill John Connor after its headquarters had been captured by the human resistance. In fact, this was precisely the reason why the second T-800 came to the past with knowledge about the T-1000, as the Resistance had found out about the latter's mission after reaching the time displacement center - and indeed, the notion of the reprogrammed T-800 being the last Terminator left in the planet at the end of T2 is why he saw necessary to sacrifice himself in order not to leave any future technology behind. In this film, however, it turns out the Resistance somehow overlooked that Skynet had also sent back Carl and his homologues at random points and dates before being defeated (as this would be the only explanation why they keep appearing in present time even after Skynet's timeline had been erased), which renders the T-800's sacrifice utterly pointless.
Terminator 2: Judgment Day had established that Arnold's face belongs now to one of the most wanted criminals in the world, as the first T-800 massacred a police station while the second got into a new shootout with the police and was involved with the destruction of a technological company (and as shown in an scene in T2, the police got closeups of the T-800's face the first time, meaning there was definitely enough material to keep a manhunt). And yet, in this film Carl had been living for some time in Texas of all places, just three states away from where both incidents happened, and apparently having no problem to maintain a curtain business nor worry that he might get discovered some day (which would have certainly ruined his new family). As if it was not weird enough, the film shows that, unlike him, Sarah has become herself a wanted criminal in all of United States despite having comparatively lesser crimes and a much more anodine physique.
Again, despite dogs are supposed to go mad in the presence of Terminators, Carl has a dog that inexplicably loves him and acts normally in his presence, presumably in order to reinforce his new image of family man by showing that an Evil-Detecting Dog somehow doesn't detect him anymore. While it could be charitably assumed that dogs eventally get accustomed if exposed to Terminators for enough time, it is still an oddity that never gets addressed, not even by Sarah, who learned about this back when she was with Kyle and should have been puzzled by it.
As in Genisys, the resistance against Legion having futuristic technology and huge resources, including IEM weaponry, thorium reactors, augmentation tech, and fancy Dragonfly aircrafts, is by itself a contradiction within Dark Fate's own timeline. The film implies the Judgement Day is imminent by showing that the 2020 versions of Dani and Grace are already around the age they were when they met after the disaster, and it is well-established that Legion's takeover evidently left humanity crippled to the point that a random factory worker with some leadership skills was the maximum figure of authority the survivors could find. How did the new resistance developed into the well-equipped, professional-looking sci-fi army (still commanded by Dani) seen in the 2042 flashbacks would almost need an entire film itself to explain, especially compared to the original duology's more realistic situation, where the resistance against Skynet never really progressed beyond scavenger state outside of the plasma rifles.