In Eureka's "Once in a Lifetime", it seemed like a joke to have Zoey be valedictorian in a future that will never happen. But to be valedictorian, she had to smarter than a school full of geniuses; a subtle way to hint that Zoey is smarter than she gives herself credit for. We later learn this to be true when she scores a 157 on her IQ test, but tells her dad it was 112.
And how did Zoey end up with a super-genius level IQ with average parents? Well, that sort of thing can happen, but Jack mentions his IQ score was 111, which he was quite proud of because he didn't know it wasn't out of 100. However, he also mentions he "wasn't even trying". What sort of person can half-ass his way through a test and earn an average score without paying attention?
This right here supports my theory that Jack is actually highly intelligent, it is just his knowledge pool and mind are geared toward investigations.
It's all but stated that Jack is actually a lot smarter than just about anyone gives him credit for. He just doesn't grasp a lot of Eureka's science (which would throw a lot of real-world top thinkers into headscracters). Probably because he just isn't that interested in raw science, once it becomes clear it's essential to performing his job, he adapts and learns fairly quickly (witness several "future flashbacks" where Jack is a lot more knowledgeable about what's going on in the town, and several times where he surprises Allison and Henry by grasping advanced science in concept, to respond to their shocked looks with "I learn stuff!") While he never really matches the geniuses in Eureka (as that would undermine the Only Sane Man humor of the show), that's probably more likely due to him having neither the time nor interest in catching up to all the various sciences that are super-advanced in Eureka, especially when he has Henry and Allison to "dumb it down" for him as needed. So yes, it seems fairly confirmed that Jack is reasonably intelligent, Zoe's mother doesn't seem at all dumb, so it's quite plausible that Zoe has the raw potential to be a genius in her own right, and the environment of Eureka allowed her to explore that side of herself. It could even be argued that Zoe's rebellious streak early in the show was do to her being bored and insufficiently challenged, while lacking the environment of social acceptance of high intelligence, in regular schools.
When the finale version of Zoe and Jack passed the one in the Pilot, they were in the sheriff's jeep instead of Carter's car, with Zoe not waving at herself as the other one did in the pilot, but with the timeline change, this could have been the way it happened in the changed timeline all along.
If Henry and Grace were working with Beverly, that would explain why Beverly turned to them to help out with the Matrix incident. Henry didn't know it, but at some point in the past, they'd worked together already.
You know how Henry's hatred of Jack for stopping him from using time travel to save Kim was apparently forgotten by the writers? In the episode "God is in the Details," Jack and Henry work together to stop the church pianist from using a dangerous device that she thinks will let her see her husband in the afterlife. Afterwards, Henry consoles the pianist, reminding her that their loved ones are in Heaven and they will be reunited with them soon. This is the point where Henry forgives Jack.
Why didn't Jo and Zane hook up in the new timeline? We learn from Taggert that in the new timeline he proposed to Jo who shot him down, this means that Zoe never talked Jo out of dating him, so Jo was never free to be interested in Zane. Why? Because in this timeline we see that Zoe herself is attracted to older men, specifically Zane, and the age difference that was the original basis for her argument against Jo and Taggert dating would seem out of character in that context.
Jack Carter is actually highly intelligent, he just does not apply that intelligence to gaining and using scientific knowledge. He instead is more focused on investigative work and problem solving. Notice how the problem of the week goes straight over his head until someone simplifies it for him, then its usually HIM to come up with a method of solving said problem even if he has no idea how to implement it(that is what the more scientific minded characters end up doing). One particular great example of this is the episode where Kevin slips some mental stimulants into Jack's coffee so Jack would not be looked down upon by Allison's brother. The first thing Jack does is read all of said brother's research and ends up coming up with methods that Allison's brother hadn't even considered. This unspoken facet to the character explains the early episode in which S.A.R.A.H. tried holding Jack hostage, claiming that there was enough data to suggest Eureka would fall apart without him(and Henry and a few others but it started with jack), He is smart enough to repeatedly figure out the Problems of the Week before more than a handful of people die, people who are reportedly invaluable to their fields of research.
Seems to be all but stated in the actual show. One doesn't get to be a US Marshal (one would assume) without some kind of ability to think and reason logically. Jack just looks dumb because he's literally surrounded by people who are off-the-charts smart, working on tech so advanced the brightest minds of the age in the real world wouldn't know what to make of it. Jack certainly doesn't have the learning and education of Eureka's scientists, but he trumps them all when it comes to on-the-fly problem-solving.
Goes back all the way to the third episode, when he keeps failing the written exam for access to Eureka's advanced weapons. At the end, Jo gives him the test in a hands-on, practical way under the guise of some tutoring, and he passes with no problem. He's not dumb, he just learns and thinks differently from many others.
In The Ex-files each of the ones hallucinating had a specific person and reason for hallucinating due to unresolved issues each had to work through:
Unlike Jack, Nathan was never shy about confessing his feelings for Allison.
Tess was there for Allison both when her first husband died and shortly after Nathan died and represented her fear of Jack dying and her heart being broken a third time.
Jo spent her whole time up to that point romanticizing her relationship with Other Zane and glossing over the negatives.
Jessica Lansky represented Fargo's insecurities about his being suddenly the boss of GD and his frustration at not being able to stand up to General Mansfield.
Adam Barlowe represented Trevor's disappointment at the military influence on Eureka and his own homesickness.
Zane's proposal to Jo, and how it got erased in the new timeline and Jo's handwringing about if they were meant to be together and if they actually had something worth getting married over. When Jo (thinking she's talking to a hallucination) throws Zane's engagement ring back at him, Zane asks why Jo has his grandmother's ring, and afterwards begins relentlessly pursuing Jo and trying to figure out what they were to each other and what happened that he's totally unaware of it. Which all makes sense when you remember that's his grandmother's wedding ring. It doesn't come up often, but family means a lot to Zane, and if he loved Jo enough to propose to her with his grandmother's ring, he loved her too much for a little disruption of the space-time continuum to get in the way.
In the episode "Reprise", one of the songs seen being acted out in the background is Nena's "99 Red Balloons" which is very blatantly about nuclear annihilation. Eureka is a town where citizens can casually own antimatter. So the clean-up that got glossed over at the end of the episode probably involved stopping somebody from nuking Eureka.
"I Melt With You" (the song that convinces Henry and Grace to build the stasis device to "stop the world" for each other) is also about nuclear annhilation, and Carter mentions "The End of the World as We Know It," stating that this is a town full of people who can make it happen. The episode runs mostly on Isn't It Ironic?, but there were certainly a few people doing decidedly less harmless or amusing things because of their musical taste.
Kim directly addresses the fridge horror inherent to the premise of "Before I Forget", noting that in addition to using the memory wiping device to steal scientific breakthroughs, her husband Jason could also have been using the device to erase her memories of a romance with Henry, cover up if he was caught having an affair, and even erase her memory of leaving him.
Taking the Historical In-Joke to its logical conclusion, if the Einstein-Grant bridge became the Einstein-Rosen bridge after the timeline changed, then that means EVERYTHING prior to the Season 4 premiere occurs in an alternate universe to our own, and it is only now that history is put "right". It may never be significant, but it is an odd thought.
The Matrix victims can exit the Matrix if they receive an intense electrical shock. Zane uses this to escape the Matrix and to help the rest of the Astraeus crew escape. In the real world, he can eject everyone, except Carter, who is plugged in at a different location. Any one of the escapees after Zane could have shocked Carter out of the Matrix, but instead they leave him to be saved by whoever is there at the Eureka IP address (an unconscious Henry and the duplicitous Beverly). Carter could have "shocked out" with minutes to go, but instead has to be ejected manually in the last few seconds before he dies.
Using a shock to get out was a dangerous technique and no one knew that Henry was unconscious. If he'd been conscious (as they would reasonably have assumed) it would have been a lot safer for Zane do what he tried to do (get the crew out and contact Henry to have him get Carter out). Shocking Carter out only really makes sense because we know things the characters did not.
Considering in the new timeline, Kevin no longer has Autism and thus no longer possesses the unique connection to the Artifact that drove everything in the first two series, you have to wonder... what exactly happened to the Artifact in the new timeline?! Does it still even exist?!
From what I recall, it was mentioned once. Somebody mentioned that the Artifact's energies had dispersed and dissipated and that the item itself was in a sense dead.
When Beverly hijacks Allison's brain, she doesn't bat an eye at repeated mentions from the Founder's Day time travelers that she is becoming Director of Global Dynamics AGAIN, even though in this timeline, Fargo succeeded Stark instead of her.
She may have been confused by it but, in the interest of preserving her cover, she couldn't exactly acknowledge that confusion (since anyone who mentioned Alison being head of GD obviously expected Alison to know about it). In addition, Beverly might not have known the specifics but she knew about the time travel (when she contacted Grant she mentioned knowing he'd travelled forward in time with people from the present). Given there were descriptions of the people he'd escaped with, she probably already knew who was involved and that this Alison was from an alternate timeline..