If you don't like what you see, buy a new mirror

Household mirrors are designed to withstand the usual attacks by toddlers/angry teenagers/flying objects and for that end are back-surface coated. This means that you have a sheet of glass on the back of that sheet is the refelctive surface. That way, the reflective coating is protected by the glass which can be conveniently wiped down. This feature however makes it unsuitable to deflect the picture of a projector.

At the point where the projector output hits the mirror it is still unfocused. Before and after the unfocused picture is reflected by the reflective surface it is refracted by the glass. This has the effect of the picture not focussing correctly on the screen anymore, also known as 'ghosting' (see picture below). I didn't do the raytracing of how this happens because I feel exploring that issue in such depth would be a waste of time.

Ghosting effect when using a household mirror. Above and below the actual object are shadows which result from the unfocused picture not being deflected uniformely. Walls and everything else are equally affected, but it's less obvious.

To resolve this issue, we needed a front-surface coated mirror. These are by far more delicate as they can easily scratch. After some research I ordered one from Knightoptical with enhanced aluminium coating (just as a reminder, it's 140mm in diameter). This is, as far as I know, the cheapest coating to reflect the entire spectrum of visible light.

Front surface coated mirror. It even comes with a protective film!

Like the previous mirror, I mounted the mirror on an L-shaped piece of scrap metal. Just make sure to fasten the nut tightly so the mirror doesn't slip.

It is thicker (6mm) than the household mirror I had before, but, to my surprise, wasn't much heavier which I thought could be problem if the right-angle joints I'm using to hold the mirror are not strong enough.

Here is the result: No ghosting anymore. You still see a slight glow or blur around the edges in the picture but that's only the camera struggling with light shining into the lens. You can still see the light overshooting the mirror, but this will be resolved soon too.

On a sidenote, I've replaced the Thorlabs 90 degree angle joints with Newport joints because you can fasten them much tighter and they easily withstand knocks and vibration. The Thorlabs joints I had to tighten every so often because the screw that presses against the post to hold it comes loose easily. Generally I choose the brand depending on who I feel has the better solution for a given part.

Thorlabs (top) and Newport (bottom) angles. As you can see the Thorlabs joint only has a screw pressing against the post to fasten whereas the Newport joint actually clamps onto the post. Both pictures are property of the respective companies.

Results

With the new mirror installed the ghosting effect is completely gone. Further, because the formerly scattered light is now focused where it should be, contrast and brightness have improved noticeably. However I still think I need to do one or two things to improve picture quality, but this is definitely a step in the right direction.