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 at 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 "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.
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 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...