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.
Is Loki a Well-Intentioned Extremist who wants power for himself to do what his father and brother can't and won't, or a Stealth Mentor who does what he does to make Odin realize Thor's flaws and give Thor the motivation to better himself? Or is he a petty tyrant craving adoration?
Is Odin a wise and just king who is simply trying to keep peace between the realms, or an overzealous tyrant who is desperate to hold onto his own power at any cost?
Cry for the Devil: Loki. On the one hand, he's a conniving, power-hungry liar, willing to betray his brother and doom him to permanent banishment while he usurped the throne. On the other hand, he's a deeply damaged young man who's convinced he's The Unfavorite, especially after finding out he was not only adopted, but from an enemy race, and is desperate for his father's approval and affection. It's made even sadder because he already had his father's acceptance and fondness, but convinced himself otherwise.
Double Standard: Abuse, Female on Male: Granted, Jane's punch couldn't have hurt Thor, but she only did it knowing he would never hit her back. If he had even without powers, audiences would probably not like that.
Draco in Leather Pants: Loki. And those pants might actually be leather. It gets even worse with The Avengers, where he summons the Chitauri to kill millions of people, and he's completely forgiven because a) he's hot, b) he's adopted, c) a popular headcanon insisting he was brainwashed. Small pockets of fangirls (usually the same ones to whom the Thor/Loki pairing is No Yay) have majorly backlashed to this, and only like Thor now.
With the sequel out, it looks like those leather pants are back.
Considering Darcy only has about a dozen lines, she's surprisingly popular with the fandom. She often gets paired with Hawkeye, Bruce Banner or Loki, three characters with whom she is never on screen. This popularity is probably down to a mix of snark, god-tazering, and Kat Dennings' own superpower.
Idris Elba's performance as Heimdall gets this. A classic case of Ability over Appearance, all but the most rabid of detractors enjoyed his performance and the hints that he's even more powerful than he lets on.
Fan-Preferred Couple: Thor/Loki, by an overwhelming margin. Probably one of the few creative works in existence for which the majority of the fandom prefers to ship the protagonist with his brother rather than the protagonist with his established female love interest.
Fans of the comics (and of Norse Mythology in general) generally prefer Thor/Sif. It helps that Sif and Thor are married in the myths (in the comics, they are notoriously on-again/off-again).
Foe Yay: There's a bit of Sif/Loki, if you look at their interactions a certain way. Probably only one-sided, though, and might be insinuated as to how Odin wanted the "joining of the kingdoms" to go. You could do worse than having your enemy's son marry into your own nobility.
Tom Hiddleston, who plays Loki, was also in War Horse. In Norse mythology, Loki took the form of a female horse and was impregnated. Yeah...
For bonus points, Tom was asked about his favorite Loki story in Norse mythology at NYCC 2011. He chose this one.
Chris Hemsworth previously played George Kirk in Star Trek, where his famous son was born during a lightning-storm in space.
An extra layer is added when you realize that Josh Dallas, who plays Fandral, is Prince Charming on Once Upon a Time and his long-lost daughter is played by Jennifer Morrison. She happens to portray George Kirk's wife... meaning that at one point Thor married his best friend's daughter.
Zachary Levi was originally cast to play Fandral, but his commitment to Chuck caused him to drop out, giving the role to Josh Dallas. Fast-forward to 2012, when Josh Dallas's commitment to Once Upon a Time caused him to drop out of the sequel. Guess who's playing Fandral? Zachary Levi.
It Was His Sled: That the manipulative mastermind behind it all turns out be Loki comes as no surprise to anyone who's even vaguely familiar with Norse mythology and/or his role in pre-existing Marvel products. Or heck, if you even saw the trailers and promotional posters where he looks Obviously Evil.
Jerkass Woobie: Loki, in spades. Despite his flaws, it's hard not to feel bad for him. Especially when he keeps making those Puppy-Dog Eyes. Even his attempt to destroy Jötunheim with the Bifröst was only to please his father and prove to be as worthy as Thor.
Magnificent Bastard: Loki. Does he orchestrate a lot of the film's events? Yes. Does he orchestrate all of them? No. Does he still make them work to his advantage and come out on top? Oh, yes. Right up until Thor's Heroic Sacrifice brought him Back from the Dead with his powers returned, Loki had won.
Some see Odin as this, since he effectively strong-armed the Jötunns into peace by turning them into a Dying Race.
Narm Charm: Half the fun of the movie is watching how dramatic all these big, goofy Norse god characters can get. In the comics, not only is the overblown drama half the fun, but it's also what makes Thor charming and different from the other Avengers.
Nightmare Fuel: The scene with Sif and the Destroyer. He's speared through the back and appears to be dead, and just when it looks like he's scrap metal, he raises his head and completely turns around to attack Sif.
Just the Destroyer itself. A giant robot thing designed to destroy. And the fact that he always appears to be scowling doesn't help.
No Yay: While there's no blood relation, Thor and Loki were still raised as brothers. Despite being the most popular ship in the fandom, some are also very averse to it. And it casts Unfortunate Implications about adoptive sibling relationships.
Colm Feore only has about two scenes as Laufey (one of them very brief), but he makes the absolute most of his screen time and proves with little more than a sinister word that he is a very threatening foe of Asgard. When he tells you to leave "while he still allows it," you'd better leave.
The S.H.I.E.L.D. agent who sees Sif and the Warriors Three walk into town radios in the following: "Uh base, we got Xena, Jackie Chan and Robin Hood..."
Ron the Death Eater: Odin gets this treatment from the fandom for how he treats both Thor and Loki.
Strangled by the Red String: This seems to be a widely held opinion on the romance between Thor (Chris Hemsworth) and Jane Foster (Natalie Portman), which really only serves to give Thor a reason to want to get back to Earth. Some have even labeled it a Romantic Plot Tumor, which is kind of funny considering that the same thing was said about Portman's character in the Star Wars prequels.
Kenneth Branagh must have realized this and says in the DVD commentary that their relationship wasn't meant to be true love, but more a mutual crush and respect based around what they represent to one another, a statement that rings a bit hollow given the sequel takes the Strangled by the Red String to greater levels.
What The Hell, Casting Agency?: There was an outcry over the casting of Idris Elba as Heimdall by comic fans who wanted to stick as closely as possible to the material, and by a self-avowed racist organization. But as Harry Knowles put it, every scene Elba is in is a resounding "THAT'S WHY!" in response to those who asked why cast a black man as a viking.