These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Big Lipped Alligator Moment: Henry gets a random scene where he sings "She Blinded Me With Science" for his alternate timeline wife, not to mention the whole laser light show, Fargo DJ'ing from his office, and everyone dancing. Then again, this was Fargo's idea. Should we really be surprised?
Somewhat Lampshaded: while trying to woo his alternate timeline wife, Henry realized that his alternative timeline self would already have used every play in his book, so he would have to do something completely out of character to impress her.
Broken Base: The new timeline in season 4. Some of the fandom enjoy the fact they're strangers in a strange land, while others pointed that it has a ton of Unfortunate Implications with how they handled New!Kevin, several relationships get Strangled by the Red String (Jo/New!Zane, Henry/New!Grace), and the question that, if the last 4 years have been effectively retconned, why should we even care about these alternate timeline inhabitants, because it's not our Eureka anymore?
Cargo Ship: As of "Momstronsity", S.A.R.A.H. and Sheriff Andy. Yes really; she even has shades of Tsundere.
Carter: "What were you dreaming about when it happened?" Stark: "You know. The usual things... wealth... power... control... over everything..." Carter: "... You dream about world domination?!" Stark: "... Not all the time."
As the show progressed, he proved to be more of a Guile Hero: he was a jerk, but he was also very loyal to Eureka, to Allison, to Kevin...
Really, he was still a Magnificent Bastard, just a bit more magnificent than before:
Carter: "Can your ego even fit in this building?! Stark: *nonchalantly checks the ceiling's height*
Moral Event Horizon: It may seem odd to apply it to an AI that technically doesn't have morals unless programmed to, but the moment at the end of season five when Matrix!Carter uses Matrix!Jenna to try and get Allie not to set off the Z-wave bomb ("Mommy, I'm scared. Don't kill me. Stay with me.") is an absolutely horrific and cruel Player Punch that plays off of Adult Fear, Children Are Innocent, and What If? to cement the viewers' hatred of the Matrix characters. The fact this is immediately followed up by seeing Matrix!Jenna matter-of-factly talk about wanting to see Mommy dead, helping Matrix!Carter strap Allie into the matrix, and heartlessly tell her good-bye makes it even worse.
Stark's message in the logic diamond in "Show Me the Mummy". Sob. His death in "I Do Over" was gut-wrenching too, but also more of a shock. It was this episode that really made it hit home.
Fargo realising that Jack lied to him in "Force Quit" and that Holly never made it out of the simulation alive.
And a couple episodes later, when Holly (whose mind is still stuck in the matrix) realizes that they can't pull her out of the matrix because she's dead. Poor Holly. That entire storyline is made of tearjerker.
They Just Didn't Care: In Season 5, Holly is brought back to life in a process very similar to cloning. Not once was there any mention of the ethical ramifications of cloning or bringing the dead back to life. Every character just acted like it was automatically the right thing to do without even discussing it. Considering the characters are supposed to be scientists, it kind of dropped the Willing Suspension of Disbelief. Any Real Life scientists would have massive qualms and endless debates about whether or not it were morally acceptable to do.
EUReKA's first two seasons centered around The Artifact and The Consortium's attempts to control it. What does the crossover with Warehouse 13 center around? Fargo traveling to South Dakota to upgrade the Warehouse's computers, and afterwards Claudia visiting Eureka to study Global Dynamic's (classified) technology.
No crossover with Alphas ever happened.
Trapped by Mountain Lions: Allison spends most of "Reprise" rescuing a man completely unrelated to the plot. subverted in that it was actually a fake memory to disguise some kind of Mind Probe put into her brain.
Ugly Cute: The little robot in "Momstrocity". D'awww!
What an Idiot: In "Reprise" even though Jo knew that the music affected the brain she still forgot to turn her radio off.
Henry. Nothing ever seems to go right for Henry, the hardest working person in the town.
While Jack is more of the Butt Monkey/Chew Toy — i.e. most of the things that go wrong for him are played for laughs — he definitely has his woobie moments. The ending of "Unpredictable" is kind of heartbreaking: Allison is reconnecting with Nathan, his ex-wife is taking Zoe back to L.A. with her, and he's all alone in the middle of a crowded room.
Jo is staring to get this treatment in the fourth season. Her relationship with Zane has been erased, and she has to start from scratch with him. Plus everyone else thinks Zane's a menace, so she takes flack for trying to defend him. Then her house gets hit by a stray rocket. Now Zoe is starting up a relationship with Zane. That last one has her just barely avoid breaking down in public.
It's alright! She gets a wonderful new house... which Zane gleefully burns down under the influence of a song.