How accurate are the wormhole visualizations in Interstellar?
TL;DR: Wormholes are entirely speculative, so they allowed themselves a great deal of leeway. In particular, they devised a wormhole metric without any mechanism explaining how it would actually exist (beyond hand-wavy nods toward a fifth dimension); they put in some more-or-less imagined astronomical objects as sources of light; and they sometimes tweaked/fudged brightness and color to make things look more interesting. But given those conditions, the photon trajectories were modeled quite accurately.
I heard they had physicists advising them while making the film
Yes. In fact, Nobel laureate Kip Thorne was one half of the original team behind the film, and an executive producer and scientific consultant on the final result, as well as the author of the book The Science of Interstellar. He's also one of the world's leading authorities on the theory of wormholes (among other things), and worked with the visual effects team to ensure that the visuals were essentially consistent with currently known physics — with some artistic license granted to make things prettier. There's a peer-reviewed paper available here (and another that may be of interest here).
Thorne was one of my PhD supervisors, and he was in the early stages of development on the movie at the time, so I got a little insight into the process. I particularly recall him saying that the objective was to present phenomena that were fantastical, but not specifically forbidden by our current knowledge of physics.
I expected to see duplicate images of things near the horizon of the wormhole. You are supposed to be able to see infinitely many copies of things on both sides of the wormhole as your eyes approach the horizon, although the copies get smaller and smaller
Multiple images presumably are present, but there's so much going on that it's hard to notice, or we see only closeups that don't actually span more than one. If I look carefully at certain frames, I can mostly persuade myself that there are multiple images of certain objects — though they are naturally quite distorted. It's also easy to see the Einstein ring, with stars zipping around it, and presumably being multiply lensed — though it's hard to pick out duplicate points of light. Moreover, the paper about the visual-effects development shows and describes multiple images in several places. But the paper illustrates them by showing a scene dominated by Saturn, so it's easy to pick out the multiple images; there are so many nebulous elements being layered into the movie that it's harder to discern what's what. Also, in a different part of the movie, we see a black hole with an accretion disk, where the multiple images are clearly visible.
Now that I think about it, shouldn't things look all red shifted and blue shifted near wormhole?
I'm not sure what you mean, but not necessarily. There are certainly some effects here, but also note that just because a photon passes close to a horizon, that doesn't mean it ends up with significantly different energy (and thus a change to its wavelength). Just imagine a photon emitted by some distant star, passing close to an ordinary (Schwarzschild) black hole, and escaping to be observed by some distant observer. If the star, the black hole, and the observer are all basically at rest with respect to each other, the observed photon will have basically the same wavelength as when it was emitted — or if it hadn't passed near the black hole at all — because whatever energy it gained on moving towards the black hole it lost on moving away from it. It is possible for the photon to gain net energy if the black hole is spinning very rapidly, or moving very rapidly relative to the emitter or observer.
As for an observer actually passing close to a horizon (or entering a wormhole), it's important to remember that the observer is also being affected. For example, when falling towards a black hole, an observer is accelerated, meaning that much of the blueshift a photon may be given will be canceled out by the redshift due to the observer's motion.
if they were realistic with the colors it could look ugly.
It is true that they weren't always scientifically precise with intensity and colors, because the completely accurate versions were less aesthetically pleasing or more confusing. This is discussed in section VI of the paper. There's also an informative blog post about that in the context of the black hole with the accretion disk here.
I think the fact that the stars appear to be printed on a 2D surface is realistic. They're all so far away that you won't see any parallax, but you will see time-varying distortion from gravitational lensing. Your brain would probably interpret that as a 2D surface. (The night sky on Earth looks like a sphere even without the time-varying distortion.)
I suspect the lack of visible Doppler shift is also justifiable. There can't be a huge Doppler shift because it would be potentially fatal. If the Doppler shift can be limited to a small value then it can probably be limited to a value so small that it can't be seen – especially when we're dealing with phlebotinum that can magically produce whatever spacetime geometry we want.
A traversable wormhole isn't a black hole. Black holes have lightlike geodesics that circle the hole arbitrarily many times, creating infinitely many images of background objects, but I don't think that needs to be true of a traversable wormhole.
Watching the YouTube video, I see a number of other problems, though.
At 0:25 one guy says "it's a sphere" and another guy says "well of course it is", and then explains that it's a circle in the 2D analogy with the folded piece of paper, so it's a sphere in 3D. That explanation is correct as far as it goes, but there's really no reason to expect the wormhole to be spherical, and there's a good reason to expect it not to be: spherical symmetry means that any path through the wormhole must pass through the exotic matter, and through whatever infrastructure is needed to keep it in place. It would make more sense to have a configuration where the exotic matter is kept away from the path you follow with your ship. The only reason Thorne et al assumed spherical symmetry in the paper was to simplify the math.
Relatedly, it doesn't seem very plausible that everything necessary to maintain the wormhole would be absolutely invisible (and seemingly intangible as well). Again this is just a simplifying assumption from the paper, not an expected property of real traversable wormholes.
They're shown orbiting the mouth quite rapidly, but then once they're "inside" they seem to have no significant angular momentum any more. I doubt they're following a spacetime geodesic. It's probably a non-geodesic path that the special-effects people thought would look exciting.
At 2:34 there's a sudden flash of light, as though they are at that precise moment entering the wormhole. Everything should be gradual and continuous. There is no event horizon in this sort of traversable wormhole solution, nor any other well-defined boundary between outside and inside. Even if there were a horizon, nothing would visibly happen there, but there isn't.
Also at that moment, there seems to be visible distortion of the ship itself. Distortion like that is not a harmless optical effect, it would pretty much be like taking a wrecking ball to the ship. The whole point of these wormhole solutions is they don't have any significant local distortion.
When they're inside there are lightning-like effects that are probably not motivated by any real physics.
At 2:58 one guy says "we're passing through the bulk". There's no "bulk" in the Thorne et al wormhole. The spacetime of general relativity isn't embedded in a higher-dimensional flat space. If they're talking about a brane-world model or something of that sort where there is a higher-dimensional spacetime, they still wouldn't be any more "in the bulk" than they usually are. The protons and electrons that they're made of are attached to the brane; they can't leave it. (Nor can they see the bulk, since photons are also stuck to the brane.)
The same guy says "controls don't work here". Again, the spacetime in the wormhole is the same as spacetime everywhere else; that's the point, that's what makes it safe to traverse. The instruments might be a bit confused, but they could still fire their thrusters, or whatever that guy was trying to do.
Starting at 3:16 there's a patch of optical distortion inside the ship (and somehow perfectly stationary with respect to it). One astronaut says "distorted spacetime" and I guess we're supposed to assume he's right. Another astronaut reaches out to touch the distortion; that's implausible because no one dumb enough to do that would qualify to be an astronaut in the first place. Her fingers visibly distort (by a huge amount). There's no way that whatever is bending the light that much wouldn't also snap or crush or shred her fingers.