After appending my 2019-04-30 update to my much older answer, the above excellent, to-the-point and from-the-trenches expert answer came in. I immediately changed the designated answer from mine to the new one. There's probably still some fun reading below in my old reply and update, though... :)
Alas, I must answer my own question: I found a very explicit example online description of someone who created a thick-film transmission hologram of a convex mirror. She (or he) describes seeing her own face clearly, even if only in monochrome. So, if I accept this description at face value, it clearly is possible to create a realistic mirror using only wave-exclusion diffraction effects. Cool!
Also, I am amused (or is it chagrined?) that this reminded me of the importance of reading long articles all the way to the end, even if you feel you already got the point. This description of an actual holographic mirror was hidden at the very end of the long posting on I mentioned in my question about how transmission holograms cannot form mirrors.
2019-04-30 Update
As noted in the comments below, the above link to an explicit description of a holographic mirror unfortunately is no longer available, not even in Internet archives.
However, this draft book chapter PDF on reflection using Denisyuk transmission holograms seems to provide pretty good coverage of the issues.
Still, as I get older I find I like finding the simplest possible explanations of things. The simplest proof that true holograhic mirrors can exist is this: You can see your own face in a pool of calm water.
Why? Well, the reason why thick film holograms can reflect light at all is because any change in refractive index in a transparent medium creates an amplitude -- a probability -- for light to be reflected back in the direction in which it came. Metal mirrors are just extreme examples of this effect, since the Fermi surface electrons in metals create a nearly 100% probability that photons will be reflected.
The quantum mechanical details of reflections works in transparent materials are covered delightfully in my favorite Richard Feynman book, QED: The Strange Theory of Light and Matter. In addition to its relevance here for understanding what is possible with holograms, I recommend QED strongly to anyone interested in understanding just how utterly and completely weird quantum mechanics really is.
Feynman discusses how properly space layers of changes in refractive index can create a surface that, at least for certain frequencies, has a nearly 100% probability of reflecting light. A holographic mirror!
Finally, take a contemplative look at this image (or a real example from your kitchen) of a roll of very layers of Mylar film:
Nearly everyone has at sometime noticed at some level of consciousness how remarkably metallic such rolls look, almost like aluminum foil. That is because even though the distances between the film layers are not wave-coherent as they would in a photographic hologram, they do collectively reflect more and more light, until the surface looks remarkably metallic... which is to say, remarkably like a mirror.
Such a roll of Mylar film thus can plausibly be construed as a crude mechanically constructed hologram, and thus a proof that at least at some level of quality, transparent materials can indeed be configured to create plausibly effective, metallic-looking reflective mirrors.
No, there's no need for screens in the movie theaters to be mirrors i.e. specular reflectors. Quite on the contrary, it's completely necessary for them not to be mirrors i.e. to be diffuse reflectors.
If the screen were a specular reflector, the light would return back into the direction of the projector and would never reach the eyes of the viewers who aren't sitting on the line in which the projector is directed. If the screen were a mirror, the viewers would only see themselves and the projector but couldn't see any magnified versions of the objects that are supposed to be in the movie.
In reality, each point of the screen – which is a diffuse reflector – effectively becomes a source of light whose intensity depends on the amount of incident light at this point and this source is located directly in the plane of the screen. So these sources of light are not images (in the sense of real or virtual images of mirrors or lens) at all. More precisely, the only image of the real "object" – the object on the screen – is formed in the viewers' eyes.
It's important for the projector to sharply illuminate each point of the screen differently, by the correct intensity of light of the right color. This requires precise optics that chooses the right directions of light rays for each point of the movie between the projector and the screen. On the other hand, each point of the screen is a diffuse reflector and much like real objects in the real world, it emits light to all directions so that all viewers may see it, regardless of the location of their chair.
Best Answer
Yeah, I know what you are talking about. There are two mirror positions that result in a dim image, one above the bright image and one below. My best guess is that there are two paths, kind of like I've drawn that both produce dim images.
The "lower" dim image is caused by photons reflecting from the air->glass transition, and the second "upper" dim image is caused by photons reflecting from the glass->air transition. In fact, this would mean there are a whole series of "upper" dim images, each getting dimer and dimmer.