I think I have a possible idea what might be going on here.
Given the type of artefacts I was seeing here, I have been looking at the graphics drivers. There seemed to be not a lot in common between MX Linux and Linux Mint. Both versions of Linux are using X11 rather than Wayland, but while MX Linux is using the Nouveau driver, Linux Mint runs a native Nvidia driver. As it hadn't been updated in a while, I upgraded Mint to the latest version (2.2 Zara), but that made no difference. On checking, I noted that the Nvidia driver had not been updated and an upgrade did not seem to be possible. I checked on the Nvidia compatibility site and found that 470 was the latest version I could use, but there were several later versions available.
I then downloaded and booted the latest version of MX Linux (25) from a USB stick. That also uses X11 and Nouveau, but later versions of various libraries. No change.
At this point I had the idea that maybe the problem is the graphics card hardware. The card is a now fairly old Quadro K4200 and having suich an older model perhaps explains why Nvidia recommends an older version of the driver package. Perhaps support for this card is no longer available in the latest versions?
To determine whether the problem is the hardware, my next step was to test in a virtual machine, because here, graphics support is provided indirectly via an emulation layer. I created and installed an MX Linux 25 virtual machine and after the installation was complete, tried running AppLab. Well, it started up normally. This meant that regardless of whether it is accessed via the open source Nouveau driver or the native Nvidia driver, the problem appears to be the graphics card. The only snag when running in the virtual machine is that although AppLab detects the UNO Q, it is unable to connect to it so it would seem that this is not a viable way of working with it.
It looks like I am going to have to upgrade the graphics card. I saw a GTX1050 on the used market in a shop yesterday. It was affordable and hopefully should fit into the case. It can also make use of the latest Nvidia driver (v580). Its a shame because I was given a GFX1060 a while back, but it had a bit of pipework sticking out of it that prevented it from fitting into the case, so I ended giving it to a mate.
What was curious of course, was that AppLab ran perfectly fine in Windows 10, so I booted into the Window 10 partition and checked what driver it was using. Turns out it was using the "Microsoft Basic Display Driver". It wasn't using an Nvidia driver at all. Not surprising, since I don't really use Windows anyway.