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.