Yes I do understand that Flash is a plugin, but Firefox (so far) won't accept its installation - is there some other step I need to take to have it recognized by Firefox?
What I'm trying to do is be able to watch MPEG-4 videos, many of which are forwarded via email. Others are links in articles and news stories.
Flash never allows you to watch directly an MP4, a developer must program a player for that.
Again, Flash is NOT a movie player. so if you already installed it
so type into the url field of firefox about:plugins
and you will see that Flash is installed.
Now, for what you want to do, Flash is not and never be done for that.
Rather a program that reads MP4 must be installed in your OS.
usually it's already possible, so you just need to go in your firefox preferences -> applications
then choose manually which program you want to use to watch MP4.
if you are still confused so my advice is to install VLC
https://www.videolan.org/
then restart firefox and with some luck you when you will click on an MP4 so VLC will open.
if it's not the case just do what I commented above