Despite his distaste for his first name, Cross is actually very well-named: Jeremiah was a prophet, and Cross knows what will happen to the Straw Hats if the events proceed without any interference.
Even better is the fact the Biblical Jeremiah failed to prevent a war, and Cross's greatest fear is failing to prevent the Marineford War.
In Chapter 20, Luffy is unaffected by B.R.O.B increasing the gravity, and even as it's warning him not to try anything foolish as it's much more powerful than him, Luffy flat out orders the entity to leave his friends alone. If you think about it a little more, Luffy is a D, and D's are the sworn enemies of the gods, especially jerkass ones.
Cross has another function on the crew: he's the lightning rod, and it's not only because he tanked the brunt of Eneru's wrath. A lightning rod diverts the electrical charge by taking it on himself to protect the house to suffer damage, just as Cross serves as a Butt-Monkey by enduring misfortune which should have fallen on his crewmates. Dipping into Fridge Horror, however, it also means Cross is likely the first to fall due to his more human physiology, best demonstrated during the events of Baron Omatsuri and the Secret Island. There, Cross is the first to be affected by Lily Carnation's spores and eventually devoured.
Vivi's Sovereign's Will was foreshadowed long before Enies Lobby: she managed to make Smoker and Eneru listen and obey to her. One could argue that Smoker doesn't count since he only bowed down when she revealed how prestigious her bloodline was, but Eneru has no such excuse.
Moria Awakening his Devil Fruit makes sense if one remembers his backstory. His first pirate crew was utterly decimated by Kaido and left him broken (mentally and physically). He then chose to create an immortal pirate crew made of the undead, along with his trump card of Oars, to take the Yonko on again. Moria would have been well on his way to get his revenge if it weren't for the Straw Hats showing up and annihilating his zombie crew. The mere thought of having a second crew annihilated while he was sedated and unable to do a thing about it was possibly a sufficiently traumatizing event to trigger the Awakening.
Perona's choice of the crow's nest for her room stems from her past at Thriller Bark when she didn't trust the rest of the Mysterious Four with its location whenever she leaves her prone body behind. It's the most isolated location on the ship, hard to get into and heavily protected (at least from ground-based assaults rather than aerial) by the crew and Sunny's defenses.
Wyvern picking his name based on him being considered as big a threat as Monkey D. Dragon makes a lot more sense than just wyverns being a type of dragon. Traditional mythology depicts wyverns as lesser dragons, smaller than normal and incapable of breathing fire, but deadly in their own right due to ferocity and certain venomous traits. Cross, in that sense, is a true wyvern compared to Dragon. While the Revolutionaries focus on more coordinated attacks on their targets, Cross instead uses the massive range of his transceiver to reveal his otherworldly knowledge to the populace, emphasizing it with his hatred of the Government and the Celestial Dragons. Through this, he's effectively poisoning the general public's image of the World Government and has started more than one revolution since he began his work. So given the fact Wyvern is Cross two years from the future, it makes sense he'd amass as much of a reputation as the most wanted man in the world.
One thing that was noted was that Shiki, even with the self-imposed restrictions, was a contemporary of Gol D. Roger, and thus still should have been at least Emperor level in terms of power therefore being incredibly hard if not impossible to defeat by the currently pre-Time Skip crew. However, there's actually some additional Fridge Brilliance as to why Shiki would go down to Luffy and Bartholomew the way he did, even factoring in his in-story reason for not using Haki.
Firstly, is time. It's been nearly 20 years since he was last seen, and while he did break his way out of Impel Down years before, it's noted that he spent most of his time in hiding, gathering power through recruiting pirates to his cause to exterminate East Blue and creating an army of monsters. The thing is however, is that it's not really shown whether he would have been able to keep up his training to maintain his Emperor-grade level of power, since the beasts would have been easily dealt with, either with Haki or his mastery of his Devil Fruit. As such, he not only would have not needed to use his powers to their fullest in any sense, but also likely would have had a hard time keeping his capabilities to Emperor level since there wasn't really anyone for him to push his limits against. Add on nearly two decades of isolation from the world, and his power could have completely stagnated, if not greatly degraded as a result.
The second aspect, ironically comes as a result of his twisted variant of his Might Makes Right Philosophy that he spouts in Chapter 57. Specifically, he believes that the strong should stand over the weak, and the weak should serve and die with no questions asked. However, as a result of this philosophy, he surrounds himself with powerful, but not as powerful as him pirates, and it is clear that he does not allow anyone to challenge him, if his reaction to Nami standing against him is any indication. But this proves to work against him, as because he is never challenged by those he perceives as weak, he never has any reason to push himself, which in tandem with the above, means that when he is finally faced with those who ARE willing to challenge him, he is underprepared and is much weaker for it, since all he is capable of doing is beating down those who are weaker than him, and it's likely he would have ran into greater difficulty if he were to ever face his old contemporaries again.
By contrast, the Might Makes Right philosophy that Kidd (and to a lesser extent, the other rookies like the Straw Hats and Barto Club) follows makes them have to earn and gain the respect of their enemies and the loyalty of their allies through their own capabilities or their collective strength, a strength that is always growing due to always pushing themselves to do better than before. As a result, not only are they willing to challenge those much stronger than themselves, but they're able to push forward in spite of the challenges because of their bonds built through their deserved strength.
In other words, Shiki's own philosophy royally screwed him over in the grand scheme of things, and he's too shortsighted and blinded by his hatred for Roger to realize it.
Cross's entire revolution revolves around him using his real-world origins by recognizing a bit of Fridge Brilliance from One Piece canon: that the World Government maintains its authority over the world in no small part because there's no mass media in the One Piece world, aside from a single government-controlled newspaper. People tolerate the rampant corruption in the Marines and the decadent malevolence of the World Nobles because they don't know it exists; any incidents where the ugly side of the World Government is revealed are quickly covered up. Through the SBS, Cross is able to circumvent the World Government's information stranglehold and tell people how the world is really working beyond the borders of their individual islands. No wonder his words are so successful, and no wonder the Five Elder Stars are so afraid of him; Cross could change the world to a greater extent than even Gol. D. Roger did, simply by peeling away the veils of ignorance that the World Government has relied upon for the past eight centuries. This is led credence when they wonder how Cross managed to get a hold of a transceiver able to access the entire world in the first place; Vegapunk had made the device before, but they had ordered him to destroy every last one, proving they feared the idea of media turning the world against them.
Throughout the Sabaody Revolution arc, Cross runs into various expies (Miror B, Yzma, and Psycho-Mantis). It is then revealed that all of them were Doflamingo's executives disguised (Dellinger, Monet, and Gladius respectively). The Brilliance is that all the expies are Antagonists just like how the Doflamingo Family are the Straw Hat's enemies.
The dugongs being deposited back on Sabaody and their lamentations about the situation is hilarious... until you realize that their position is ship's guards. They will be all that's standing between the Thousand Sunny and the endless tide of opportunists trying to sink it for the next two years.
The Grand Line Funeral Bouquet is a variety fruit basket. When a Devil Fruit user dies, their Devil Fruit reincarnates in an appropriate type of (likely nearby) fruit. Do the math.
Word of God says that Cross was pulled into the One Piece World when his future knowledge only extended as far as Chapter 800, the tail end of the Dressrosa arc. Meaning that they're going to enter the Yonko Saga, a battle against at least half of the four strongest pirates on the Grand Line, in a possibly altered timeline (for better or worse), more or less blind. Keep in mind the Nightmare Fuel that we've seen so far of Big Mom and Kaido. Eep...
Nami's reaction when Cross reveals how frail he is at the Twin Capes: when she hits Luffy or Zoro, they treat it as a small annoyance. Cross can't. And she went for the hit, and laid him unconscious for several minutes because she thought he could take it. What if she had hit harder? You can hear the question in her mind when she realizes she could have accidentally killed one of her crewmates.
During the Rainbow Mist special, Cross reunites with one of his friends from the real world. His friend reveals he'd been sent to JoJo's Bizarre Adventure by a BROB of his own. Cross's situation of being thrown into a fictional universe by a sadistic, god-like entity is scary, but the idea that there's more of them doing the same thing makes it horrifying.
What's worse, Cross' friend has apparently been in JoJo since Part 3! For context, Cross is 19, his friend is about in his 40s-50s, and when he first appears in the special, he's hunting down Pucci!
Ever wonder why Buggy the Clown, a guy who sailed the Grand Line with Gol D. Roger, would wind up fleeing into the safety of East Blue — widely acknowledged as "The Weakest Sea" — and hiding there instead of going after One Piece himself? Well, in this version of the setting, he saw his whole first crew eaten alive by Lily Carnation. In all likelihood, he was scared out of the Grand Line entirely by the trauma; despite his claims of claiming One Piece when they first met, Buggy probably never intended to go back near the New World again if he could help it.
Which raises another thought: could Buggy's weakness be a result of his skills naturally declining through a lack of a challenge combined with sheer trauma at what he went through on Omatsuri Island? Sort of an inversion of Took a Level in Badass? And with Lily Carnation now dead... could the catharsis give Buggy a chance to heal from his trauma, and maybe start getting back in the game for real?
Throughout the Sabaody Revolution arc, Cross runs into various expies (Miror B, Yzma, and Psycho-Mantis). It is then revealed that all of them were Doflamingo's executives disguised (Dellinger, Monet, and Gladius respectively). Not only that, but Gladius (who was dressed as Psycho-Mantis) correctly guesses that Cross was thinking of a video game, a term he shouldn't know. Word of God later confirms that Gladius discerned the term with Observation Haki.
Cross goes through an in-universe example when wondering how potent cancer is in the One Piece world while seeing Sanji and Boss light up their own cancer stick. He initially dismisses it because of how much faster people regenerate compared to his world, until he recalls that cancer starts because cells in the body mutate and no longer die, which could be enhanced by the One Piece residences' healing factor.
Meta in-universe Fridge Horror: Gol D. Roger was going to die from an unspecified incurable disease. Keep in mind that cancer is genetic as well as environmental. If they manage to save Ace from execution he might end up developing what Roger had.
In canon, Big Mom is furious with Lola for running out on her politically important Arranged Marriage with Prince Loki of the giants. Unfortunately, while Lola has escaped her mother's domineering influence, (and is no longer oblivious to her mother's cruelty), what about poor Chiffon, who received all of the Misplaced Retribution? All the more reason to worry now that in this fic, Lola called out her mother and dared her to try and get her?