Would a wormhole in space look like anything at all? In movie "Interstellar", the wormhole is elaborately depicted as a sphere, complete with an explanation about why it is spherical, and as it is approached, it looks like a sphere containing fabulous galaxies etc.
While it appears to make sense that the spatial manifestation of a wormhole would be spherical, I can't see why a wormhole would "look like" anything at all.  
If I have anything approaching a reasonable mental model, a wormhole is simply a region of space that has the property that if you traverse it you arrive at a different place in space than your apparent 3D trajectory would suggest.   But it's still "just space".   It doesn't have a "surface" or a distinct "entry point" or any particular features at all, does it?    

Note: I appreciate that nothing in "Interstellar" should be taken as a representation of actual real world physics - it was simply the thing that triggered the question about real physics!
 A: The site you linked to on the modeling of what theoretical wormholes would look like shows two reasons a wormhole could be visible: 1) the scene you see through it might not match the surroundings on your end, and 2) there's a lot of distortion of the image of any objects which from your perspective are near the "edge" of the wormhole. 

Both effects seem to be at play in the interstellar wormhole, if you look at the large image here. For 1), the image shows a bunch of nebula and a greater overall density of stars in the space on the other side, so that makes it stand out against the starfield on our side. And for 2), you can see that there's a lot of visual distortion in the shapes of the nebulas and things near the circular edge, not much at the center.
Kip Thorne, the physicist who was the science consultant for the movie, says in Chapter 15 of The Science of Interstellar that there were three main adjustable parameters or "handles" that they could use to find a look for the wormhole that Christopher Nolan and effects supervisor Paul Franklin liked best: the wormhole's radius, its length, and something called the "lensing width" which is determined by the curvature of space outside each "mouth". But for any given values of those parameters, they used the real theoretical predictions of Einstein's theory of general relativity to determine the wormhole's appearance:

Just as I had done for Gargantua (Chapter 8), I used Einstein's
  relativistic laws to deduce equations for the paths of light rays
  around and through the wormhole, and I worked out a procedure for
  manipulating my equations to compute the wormhole's gravitational
  lensing and thence what a camera sees when it orbits the wormhole or
  travels through it. After checking that my equations and procedure
  produced the kinds of images that I expected, I sent them to Oliver
  and he wrote computer code capable of creating the quality IMAX images
  needed for the movie. Eugénie von Tunzelmann added background star
  fields and images of astronomical objects for the wormhole to lens,
  and then she, Oliver, and Paul began exploring the influence of my
  handles.

The book also includes some pictures showing how the visual appearance of the wormhole changes when these three "handles" are adjusted in various ways. In particular he shows that the amount of distortion of objects near the visual edge of the wormhole depends on the "lensing width", which measures the sharpness of the transition from the throat to the space outside the wormhole's mouth--if transition is sharper, so the space outside becomes nearly-flat at fairly short distances, then there's a thinner region of distorted shapes at the edge.
Finally, at the end of the chapter Thorne notes that although they modeled the external appearance accurately, for the trip through the wormhole, the visual effects people took some artistic license, creating "an interpretation informed by simulations with my equations, but altered significantly to add artistic freshness."
A: There's no reason for a traversable wormhole to be spherically symmetrical; in fact, it seems very unlikely, even by wormhole standards, that it would be.
The reason is that if there is spherical symmetry, then the exotic matter, and whatever containment structures are necessary for it, are spherically distributed, which means they block the wormhole on all sides and you must pass through them to traverse it. Interstellar seems to completely ignore this problem. Their ray-tracing simulation treats the wormhole as a vacuum (which it isn't), or at least treats the exotic matter and containment machinery as entirely invisible and intangible. I suppose that's not impossible—they could be made of shadow matter—but it adds another layer of farfetchedness to an already farfetched idea.
Kip Thorne's original paper with Michael Morris (unpaywalled) spends a lot of time analyzing the forces experienced by a ship traversing the wormhole, because survivability of the trip puts constraints on the geometry (section II.E). This analysis is only necessary because their assumption of spherical symmetry makes it impossible for the ship to evade the regions of high curvature.
In section II.F.4 they suggest running a small tube of vacuum through the sphere. But I think you may as well just forget about spherical symmetry entirely and make a wormhole with corners:

The middle part of this manifold, through which the spaceship would pass, is flat. All of the exotic matter is at the ends, and you can put a solid containment structure around it without blocking the ship.
The result of extending this to 3 spatial dimensions is the sort of looking-glass portal that has been a mainstay of fantasy stories for ages:

The exotic matter is in the frame, and there is no significant curvature elsewhere (and in particular, no distortion of light passing through the center).
It's almost certainly impossible to make such a thing, but it seems a lot more plausible than what's shown in Interstellar, or in Hypnosifl's answer.
