Judging from how much is written on various websites, laser cutter mirror alignment causes a lot of difficulty. I did not think it was hard until about two weeks ago when my Beambox suddenly lost its alignment and I couldn’t get it back. These are the alignment shots that I collected:

The instructions tell us to align points A and C to get the upper-left coincidence, then A and B to get the coincidence on the upper right. That worked well. But when I collected test burns for point D, it became clear that something wasn’t right.
I started thinking that something else must be wrong, something like a warped guide rail, or a twisted gantry, a loose belt, a cable snagging and rotating the cutting head as it got pulled. Yesterday, I got out a spirit level and checked the Beambox’s support table. It was level, so that wasn’t the cause. I tried checking some of the angles for squareness. They seemed to be square but I don’t have a suitable square on hand (I improvised a bit) to be absolutely sure.
Today, I tried the Beambox again, and somehow everything is working. I don’t know why. I haven’t done anything to make it happen! I realigned (only small adjustments needed) and got these alignment shots:

The holes are smaller this time because I turned the laser power down to 15%. I find the smaller holes easier to work with.
These are the shots through the lens, set at four different heights.

They’re slightly different from each other, which means that the beam is still the tiniest bit off-centre. It is probably not coming directly downwards, but at a very small angle off the vertical. This is close enough for me, though, at least for now. I picked the second one because it’s the roundest. I think this indicates minimal cutoff from the sides of the exit aperture.
I ran a test cut, another one of my felt coaster series. It came out just right.