Can anything be done about the ‘unmet dependencies/broken packages’ for applications that cannot be installed? (e.g. “libavcodec58” is often mentioned)
As I explained in the Installation Instructions, MintPPC is based on Debian sid, which is the unstable version of Debian. There are no longer stable releases for PowerPC anymore, as Debian dropped support. What we are therefore dealing with is Debian sid, which very often has broken packages. The only thing you can do is wait until the packages are no longer broken. Once you have been able to install a package, this package will keep on working, as your Debian system will not install packages which will break the installed packages. If you are really impatient, you might want to build all the required new packages yourself. So, as an example, audacious was installable a few weeks ago, now not anymore. If you would have installed audacious then, you would have audacious working. Now, you have to wait.
As an example, you were referring to libavcodec58, this package is built from ffmpeg source. If you look at that source package in buildd.debian.org, you can see that this package failed to be built on powerpc 7 days ago:
https://buildd.debian.org/status/package.php?p=ffmpeg&suite=sid
In exceptional cases, I am willing to try to build packages myself, if a package remains unbuilt for a long time. Normally though, that is at least my experience, such packages become available again after a few weeks. As I said before, once you have a package installed, it will keep working and will not be made broken again.
So, in essence, do I just need to run 'apt update' and 'apt upgrade' on a regular basis to check if packages are no longer broken?
sudo apt update
sudo apt install audacity
or whatever you want