Anyone thinks the color grading looks off?

Could it be because it's from film, not digital?

Yep I noticed it too with the trailer. But maybe that's just the trailer, because the colors in the prologue (in IMAX) looked really beautiful and realistic.

65mm film has more image and color quality than regular 35mm film. Also Nolan is going for more of a grand spectacle approach as opposed to Spielberg.

From Wikipedia:

To achieve a tone and quality that was true to the story as well as reflected the period in which it is set, Spielberg once again collaborated with cinematographer Janusz Kamiński, saying, "Early on, we both knew that we did not want this to look like a Technicolor extravaganza about World War II, but more like color newsreel footage from the 1940s, which is very desaturated and low-tech." Kamiński had the protective coating stripped from the camera lenses, making them closer to those used in the 1940s. He explains that "without the protective coating, the light goes in and starts bouncing around, which makes it slightly more diffused and a bit softer without being out of focus." The cinematographer completed the overall effect by putting the negative through bleach bypass, a process that reduces brightness and color saturation. The shutter timing was set to 90 or 45 degrees for many of the battle sequences, as opposed to the standard of 180-degree timing. Kamiński clarifies, "In this way, we attained a certain staccato in the actors' movements and a certain crispness in the explosions, which makes them slightly more realistic."

I didn't see anything that was odd. Reminded me of Saving Private Ryan or Enemy at the Gates.

Whatever you are, be a good one.

I think it's maybe because we're too used to seeing flat and uninteresting digital films whereas this is 65mm film and looks quite similar to Paul Thomas Anderson's The Master, if not deliberately underexposed for more "grittiness." Honestly the color saturation and contrast looks far better than most films I've seen lately. But nevertheless, it's also worth noting that trailers usually receive different color timing as opposed to the final product in order to create a unified "look."The final film will receive more specialized timing.

Personally, I think the way it's been coloured is more in line with the way in which Nolan tells his stories and how he directs, his films have always been about core emotion and drama between characters rather than elements of violence.

Saving private Ryan went about the colour grading by desaturation to make it add to the grit and 'hopelessness' of the war they're charging into,

Dunkirk, I feel, makes its colours more vibrant to represent the hope of them trying to escape it.

Just my two cents, can't wait for the film either way :)

Trailers are graded separately, and often don't reflect the look of the finished film.

There is a massive amount of "fiddling" with colour these days compared to a decade or more ago.