In the pilot, while arguing about the effectiveness of Fitz's "Night-Night" gun, Simmons says that "I'm not Hermione! I can't create instant paralysis with that!" The latter part of the comment is a reference to the scene where Hermione went Petrificus Totalus on Neville. Mind you, Simmons' appearance seem to deliberately invoke the image of Hermione from the movies on a regular basis.
In "Repairs", when Skye gets frustrated with FitzSimmons not letting her touch anything in their lab because she hasn't taken the required classes, she refers to the Academy as "your stupid S.H.I.E.L.D. Hogwarts" in retaliation.
In "...Ye Who Enter Here", Skye refers to what the Obelisk can do as something out of Harry Potter.
"Love in the Time of HYDRA" has Hunter refer to the "real" SHIELD as "Hufflepuff".
In "0-8-4", Ward uses a staff weapon that releases a head-high shock wave of energy when it's shoved into the ground; it's almost the exact same move and effect as the one Simon uses to rescue River in the opening of Serenity. It even has a component that launches into the air and produces the wave.
In "The Only Light in the Darkness", Fitz is given the desert island scenario question on the polygraph test (he's asked what he'd hope/expect to find if he was washed up on a desert island alone with a sealed crate). He answers "Simmons", recalling the iconic Girl in a Box reveal from the Firefly pilot episode.
Additionally, there's the entire layout and design of The Bus. The design seems exactly like something you'd expect to evolve into a Firefly-class ship, with the thrusters the same, the bay the same, the whole idea of staircases in the bay the same, and generally, it's a far more fancy, but plane-y precursor to the Firefly-class ships of Firefly.
A very easy-to-miss one. In his first appearance, Col. Glenn Talbot says "you and your men can be on your merry", a paraphrase of one of Mal's lines from "Serenity"
Another subtle one to the Whedonverse: Simmons's crush on Mike Peterson only lasts an episode, but it serves as an oblique Shout Out to Angel: in both shows, a socially awkward genius (who happens to be a young, brunette woman) develops a crush on a character played by J. August Richards.
One scene in "The Hub" showing the interior of Fitz's bunk on the Bus reveals he's personalized it a bit with a miniature TARDIS. This wasn't a random shoutout either: the episode aired a couple weeks before the 50th anniversary of Doctor Who, and in fact this was also done on several British television programs in tribute, including an episode of Holby City that aired the same day as the SHIELD episode.
When Simmons is put through a polygraph test in "The Only Light in the Darkness", one of the questions is what she'd hope to find if she was washed up alone on a desert island with only a single, sealed crate. Her answer, after a bit of thought, is the TARDIS.
The Who references obliquely count as additional Marvel references, too, as Marvel published a Doctor Who comic strip in the UK for many years and the Whoniverse even has its own official Marvel Universe number (Earth 5556).
In "The Things We Bury", Skye runs down the code names for Coulson, Triplett, and Fitz during their mission. One of them (almost certainly Fitz) has apparently chosen "Time Lord".
In "4,722 Hours", the video Simmons plays on her phone of team Coulson celebrating her birthday shows a cake in the shape of a TARDIS.
In Coulson's dream-flashback to Tahiti in "The Well", he and his masseuse have an exchange reminiscent of Dollhouse:
Coulson: Did I fall asleep? Masseuse: For a little while...
The warehouse scene in "Shadows" has many parallels to the warehouse from the Indiana Jones franchise. At the beginning of the episode, the crates the Howling Commandos seized from HYDRA have the "palm tree and swastika" seen in Raiders of the Lost Ark, though the location given is far from the tropics.
Lance mentions a line from Star Wars in "Shadows" when he asks whether Garrett went to the "dark side", except Coulson added that he went nuts as well.
Also referenced in "Eye Spy" when Coulson sounds a lot like Obi-Wan talking about how he lost Vader to the Dark Side. The music even sounds close. Skye references it directly in case you missed the not very subtle reference.
Bobbi is later seen in a Star Wars t-shirt.
And Billy Koening has a closet full of Star Wars clothing.
Then you have Cal. Evil for much of the second season and utterly, blindly loyal to the person who turns out to be the real Big Bad. In the end, to save his child, grabs said Big Bad and lifts them just like Vader did to the Emperor. Not to toss them into a shaft, though; to give them a broken spine.
Coulson: Help me, Obi-Wan Kenobi! You're my only hope!
Coulson's classic Corvette "Lola" turns out to have machine guns hidden behind the headlights, much like a certain other spy's Aston Martin DB 5.
Even HYDRA's getting in on it - in "Making Friends and Influencing People", when Agent 33 is being brainwashed:
Mr. Whitehall: Mr. Bakshi, let's go again. Mr. Bakshi: Where do we start? Mr. Whitehall: At the beginning! Like the song says - a very good place to start.
This one is doubly funny once we learn Whitehall was an actual World War II German Nazi, so it's ironic that he would enjoy that play.
In "A Hen in the Wolf House" Skye realises that Hunter has been drinking fairly heavily during the mission. When he argues that he had to do so in order to maintain his persona, she snarks that he must be undercover as Ron Burgundy.
Skye attempts to insult Hunter's British accent by nicknaming him Trainspotting. (Hunter immediately shoots this down by exasperatedly pointing out that Trainspotting is Scottish, whereas he's English.)
Kyle MacLachlan portraying a man who lost his wife, forced to abandon his children, and was thrown into a one-man obsessive mission? Not unlike the eventual fate of Dune's Paul Atreides, whom he portrayed in the David Lynchadaptation.
In "The Things we Bury", the bus decloaks when landing in Hawaii, using the same sound effect of Klingon and Romulan cloaking devices in Star Trek: The Next Generation.
The Kree device on Gonzalez's carrier is behind door 47.
In "One of Us" Coulson is heard talking to Agent Broyles, sharing a name with a character from Fringe, another show featuring strange science, alternate worlds, and people with "gifts".
There being an alternate SHIELD seems quite similar to there being an alternate Fringe team, particularly in logo and building structure.And one of its members is none other than Charlie.
The restaurant holdup at the start of "Love in the Time of HYDRA" sort of resembles Pulp Fiction.
In "One Door Closes", Skye notes that she regrets having watched Paranormal Activity before she was placed in an isolated cabin at night.
The Bus's flight number was "SHIELD 616". 616 happens to be the multiversal number of the mainstream Marvel Comics universe.
Said appearance seems to be inspired by the similar prickly monster girl Shuna Sassi from Nightbreed.
It's hard not to look at thisOner action sequence with Skye and not think the fighting style was directly influenced by John Wick.
When Cal finally takes his serum, he falls ill and drops behind a table, popping back up onscreen having fully changed into a deformed monster. This is a shout out to the classic trick used to obscure Jekyll's transformation in the old Dr. Jekyll and Mr. Hyde movies - a double reference, as Cal's supervillain identity in the comics is Mr. Hyde.
In "Devils We Know", Mack compares Lash to a great white shark.
Mac: It's like a great white shark. Built to eat, sleep— Daisy: And kill. Mac: I was going to say "make little baby sharks", but then Jaws was probably twenty years before you were born.note actually only thirteen years
The year they were sent to the mysterious planet might not be a 2001: A Space Odyssey reference by itself, but combined with the portal artifact that leads there being called the Monolith, it's got to be deliberate.
Season 3's Advanced Threat Containment Unit (ATCU) sure sounds similar, at least in name if not in function, to the Asset Containment Unit.
In "Many Heads, One Tale,":
Hunter's hoodie and attitude while pretending to be a Boxed Crook hacker makes him very similar to Elliot Alderson in Mr. Robot.