I don’t know anything else, but I have been using firefox for a while, and I can’t think of any times where a website didn’t work. Seems like a almost perfect drop in replacement for chromium currently, just needs people to do it.
There are some extensions that are only available for Chrome, but beside that this compatibility issue mostly happens with government sites and stuff like that. Since in their case it’s you who want something from them and not the other way around, they’re free to only check compatibility with something and say that anything else might not work.
Most of the time I stumbled upon such sites requiring IE, but that era seems to be over by now, fortunately.
I’m sure there’s a few sites that don’t work on Firefox, but I’ve definitely never ran into one, so its gotta be a very very small issue.
Regarding extensions, that is an issue I’ve had, but it turns out that some extensions can be ported to Firefox relatively easily. I don’t have a clue how to write browser extension’s, but all I had to do was make a mozilla developer account and you can convert automatically them there. There are certainly some (or most, not sure) that would require someone to manually port to Firefox though.
All in all, its almost a perfect drop in replacement.